I wrote a post on the time element that commented on in the OP but decided to not post it. From the OP:

Improbable events must happen because time is moving forward.

I’d like to highlight the following from the linked wikipedia article.

All the events in {\displaystyle {\mathcal {F}}} that contain the selected outcome {\displaystyle \omega } (recall that each event is a subset of {\displaystyle \Omega }) are said to “have occurred”.

They “have occurred,” but their probability is not 1.0.

If you think that the absolute probability of life originating on earth is miniscule, then the absolute probability that life exists on earth should also be miniscule. But that latter miniscule number appears in the denominator when you calculate conditional probability.

Or, looked at the other way, if life on earth did not originate here then it came from elsewhere. And, at present, there is no evidence to support this possibility.

I think there is some imprecision in the language here You are talking about something that has happened as if it will happen. Did you mean to say that if you pull out one winner that you did get an improbable result?

I think this is the point I’ve been attempting to make. If you pull out one winner you got a highly probable result. p=1.0. This is assuming of course that pulling out a winner is inevitable.

Could we discuss the case where the lottery may or may not have a winner? Simply declaring that there will always be a winner could be seen as begging the question.

If the lottery has 100 million tickets and only one is sold and that ticket happens to win, does that require a special explanation?

FWIW, I agree with you and Neil that for science we should be careful to specify the nature of the probability model and how it applies to the events whose probabilities we are are estimating.

Then there is the separate issue of how one interprets probability: eg as limitations in human knowledge versus as independent of people’s knowledge. That too can vary by context (eg QM versus just about anything else). That issue was the one I was referring to in the lottery example.

Please consider the following passage by Richard Dawkins:

Let us hear the conclusion of the whole matter. The essence of life is statistical improbability on a colossal scale. Whatever is the explanation for life, therefore, it cannot be chance. The true explanation for the existence of life must embody the very antithesis of chance. The antithesis of chance is nonrandom survival, properly understood. Nonrandom survival, improperly understood, is not the antithesis of chance, it is chance itself. There is a continuum connecting these two extremes, and it is the continuum from single-step selection to cumulative selection. Single-step selection is just another way of saying pure chance. This is what I mean by nonrandom survival improperly understood. Cumulative selection, by slow and gradual degrees, is the explanation, the only workable explanation that has ever been proposed, for the existence of life’s complex design.

Dawkins, Richard. The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design (p. 450). W. W. Norton & Company. Kindle Edition.

Is he not arguing that the statistical improbability of life does require a special kind of explanation?

Of couse it isn’t. Whatever you think about how unlikely it is for life to originate, surely we can agree that life originating inside the core of the Sun, is less probable, than life originating somewhere on Earth where conditions are milder and less hostile?

In either case, the probability might be very low, but one is clearly much less probable than the other. The probability thus depends on some prior conditions, hence it is a conditional probability.

I don’t know the context for your quote so I cannot say what Dawkins motives are.

But there is nothing special about the scientific explanation of life, when we have one. We will have a causal model and that model will involve a probability distribution for its predictions. We then can apply that distribution within the context (eg background conditions for exogenous variables). . We make and justify assumptions for unknowns that enter into the context needed to calculate the probability. Whether we choose to call the result improbable is a matter of how we choose to define that adjective. Is .05 improbable?

Note that I am using probability distribution to include the degenerate case which assigns one event 1 and others zero (that assumes a discrete random variable in the model).

We considering ‘‘perfect’’ condition like Earth, I never talked about the probability of life originating on Pluto, but only on Earth. in that case, since I all conditions are met. then I do not need to take into account any condition. My point is even if all conditions are met you still need to calculate the probability of forming proteins and all stuff for a cell. If conditions are met it does not automatically mean life is inevitable.

My point is even if all conditions are met you still need to calculate the probability of forming proteins and all stuff for a cell.

How do you know what the simplest, or the first, or the most probable form of life is? What do you know about the conditions that are most favorable to it’s origin?

If conditions are met it does not automatically mean life is inevitable.

Sure, but you still have to know what the conditions are, and what exactly you’re attempting to calculate the probability of.

you are confusing environmental conditions and minimum requirements for a cell to be alive.
For environmental conditions, I said, we are assuming ‘‘perfect’’ conditions (by the way, I had also astrobiology course in my studies, I am not saying something what I do not understand).

and for minimum requirements for a cell to be alive, you can test in the lab, but a single protein is not a life, you can calculate the probability of protein by constraint its chain 100, 150, 500, you will get probability each of chain

That still doesn’t tell you anything at all about how many other possible proteins or chains can support life. You’re still missing that critical piece of information which make all these “it’s too improbable” claims useless.

I’m asking you to explain how you know what both of those are?.

A) What are the most conducive environmental conditions for the origin of life?
B) What are the minimum requirements for life? Not “a cell to be alive”, but life, any and all possible forms of life.

Is a cell the simplest form of life, and how do you know how such an entity could or could not form?

For environmental conditions, I said, we are assuming ‘‘perfect’’ conditions

Yes I understood that just fine. I’m asking how you know what those “perfect conditions” are?

and for minimum requirements for a cell to be alive, you can test in the lab

What qualifies as a cell, and is that the first stage in the origin of cellular life? How do you know?

but a single protein is not a life

I’m not saying it is. I don’t know what the simplest form of life is. Do you? Then what is it and how do you know that?

i said elsewhere Science cannot observe outside observable nature what might or might not be other possibilities. I am talking about only EXISTING proteins that suppot life, not unobservable-unknown possibilities. When you bring into ‘‘possible outcome’’ unobservable-unknown possibilities that is not science. We are calculating probabilities only with respect to EXISTING life form, not unobservable-unknown life forms. Doing that i am within boudaries of Science, When i start to introduce into my probability equation unobservable-unknown life forms then i am deviating from science into mytology, fairy-tale stories, fiction stories.