When you prove something in mathematics, at very least you implicitly assume you have made no mistakes anywhere, are not hallucinating, etc. Your "real" subjective degree of belief in some mathematical proposition, on the other hand, must take all these things into account.

For practical purposes the probability of hallucinations etc. may be very small and so you can usually ignore them. But the OP is right to demonstrate that in some cases this is a bad approximation to make.

Deductive logic is just the special limiting case of probability theory where you allow yourself the luxury of an idealised box of thought isolated from "real world" small probabilities.

edit: Perhaps I could say it a different way. It may be reasonable for certain conditional probabilities to be zero or one, so long as they are conditioned on enough assumptions, e.g. P("51 is a prime" given "I did my math correctly, I am not hallucinating, the external world is real, etc...")=1 might be achievable. But if you try to remove the conditional on all that other stuff you cannot keep this certainty.