In cases like this where we want to drive the probability that something is true as high as possible, you are always left with an incomputable bit.

The bit that can't be computed is - am I sane? The fundamental problem is that there are (we presume) two kinds of people, sane people, and mad people who only think that they are sane. Those mad ones of course come up with mad arguments which show that their sanity is just fine. They may even have supporters who tell them they are perfectly normal - or even hallucinatory ones. How can I show which category I am in? Perhaps instead I am mad, and too mad to know it !

Only mad people can prove that they are sane - the rest of us don't know for sure one way or the other, as every argument in the end returns to the problem that I have to decide whether it's a good argument or not, and whether I am in any position to decide that correctly is the point at issue.

It's quite easy, when trying to prove that 53 must be prime, to get to the position where this problem is the largest remaining issue, but I don't think it's possible to put a number on it. In practice of course I discount the problem entirely as there's nothing I can do about it. I assume I'm fallibly sane rather than barking crazy, and carry on regardless.