Aside from the question of whether the calculation was good that isn’t really a relevant probability. Your argument appears to be that since the chance of a random protein having a β-lactamase fold is low we should jump to the conclusion that there is an intelligent agent causing antibiotic resistance in bacteria.
But, of course, it isn’t a random protein. Is it? It’s a modification of a protein that the bacterium already produced. We don’t have a single shot at producing a β-lactamase fold from scratch - we have very, very many attempts at producing a β-lactamase fold by modifying one of the many proteins already produced. And we certainly can’t restrict ourselves just to the bacterial species that actually succeeded in doing so, either.
If you think you can calculate that probability then go ahead - but Axe came nowhere close to doing so.
By “normal conditions” you mean in objects known to be built by humans. That is already a very significant difference. Given that we have no manufacture - the various flagella grow naturally - nor do we have a known entity capable of creating or implementing the design, the inference is not so clear. (I should note that I am not insisting that a “known entity” needs to be any more known than “a human”). Certainly not clear enough to justify inventing an ad hoc designer.
Now evolutionary theory is a viable theory that explains a great deal. If the self-styled “design theorists” actually came up with a design theory that could replace or even augment evolutionary theory they would have something. But so far they don’t seem to be even trying.