Some ID proponents claim that improbable events need a special explanation other than ordinary, run of the mill processes. This simply isn’t true, and is in part due to common biases in human intuition.
The reality is that extremely improbable events are inevitable. Improbable events must happen because time is moving forward. In many systems there are nearly an infinite number of possible outcomes that could occur, and one of those outcomes MUST occur as time moves forward. It is a bit like Schroedinger’s cat. The cat has to be alive or dead when the box is opened. A result must occur.
The same logic applies to genetics and evolution. There are nearly infinite possible evolutionary pathways that could occur, and due to the arrow of time some of those pathways must occur. Of the nearly infinite number of possible functional sequences that could evolve, it is inevitable that one of those extremely improbable functional sequences will evolve. For example, it has been estimated that there are 2.3 x 10^93 possible functional sequences for cytochrome c (reference), and that is just for the specific cytochrome c isoform we are familiar with. That calculation doesn’t take into account the possibility that there are other proteins with very different protein structures that could still have function equivalent to known cytochrome c. Of those numerous possible functional sequences we only see a tiny, tiny fraction in actual species.
We could also use the lottery to help illustrate the inevitability of improbability. In our example, the chances of winning the lottery is 1 in 100 million. There are exactly 100 million tickets sold in each drawing, and every drawing has a single winner. The last 5 winners are John, Susan, Sam, Leslie, and Stephanie. I think most people would say that you will inevitably have winners in a lottery when enough tickets are sold, but the results are still extremely improbable. The chances of those 5 specific people winning is 1 in 100 million to the 5th power, or 1 x 10^40. Do we need a separate mechanism to explain why some people lost and others won? No. So why would we think that a beneficial mutation needs a difference explanation than a neutral or detrimental mutation?
There is also a different lesson in all of this. We can learn a lot about how very natural human biases can affect our understanding of probabilities. We humans tend to put more importance on good occurrences than bad or inconsequential occurrences. Gambling addiction is often fed by this same tendcy where addicts will only remember the big jackpots and not all of the losses. Due to this asymmetry, we often think that good and bad things are somehow different from each other, but they are often the product of the same process. The simple fact is that the probability of an event that has already occurred is 1 in 1, because it happened.