Beautiful! Of course, no finite probability could ever prove that no solution exists, but being able to say that the odds of a solution are 10^-31 is, for all practical purposes, a guarantee there is none.
Well, having such a probably could indicate that the possible solutions "could" happen from 10^31
What a lot of people don't know is that the theorem was already proven for several expoents before the final solution (including for 3 and some others - and multiples of those cases)