Yes, obviously P(respectable mathematician claims a contradiction | a contradiction exists) > P(respectable mathematician claims a contradiction | no contradiction exists), so it has definitely moved my estimate.

Can you roughly quantify it? Are we talking from million-to-one to million-to-one-point-five, or from million-to-one to hundred-to-one?

I'm not sure if this line of debate is a productive one, the issue will be resolved one way or the other by actual mathematicians doing actual maths, not by you and me debating about priors (to put it another way, whatever the answer ends up being, this conversation will have been wasted time in retrospect).

Sorry if I gave you a bad impression: I am not trying to start a debate in any adversarial sense. I am just curious.

Furthermore, not wanting to be unfair to Nelson, but the fact he's working alone on a task most mathematicians consider a waste of time may suggest a substantial ideological axe to grind (what I have heard of him supports this thoery) and sadly it is easier to come up with a fallacious proof for something when you want it to be true.

Of that there's no doubt, but it speaks well of Nelson that he's apparently resisted the temptation toward self-deceipt for decades, openly working on this problem the whole time.