My estimated probability is too low to consider alone without additional evidence. I like this probability. If you require a number, 1/10,000,000.
Now, I currently appear to be typing with both hands, and there is nobody else in sight. Does this evidence lower the probability that my left arm is paralyzed as much as you might expect? If my left arm is paralyzed, there's a good change that this is just a rationalization.
See if you can think of a statement S that contradicts a statement of high probability such that no observable phenomenon is evidence against it. (Of course, nothing will be evidence for it, either.)
Followup to: The Strangest Thing An AI Could Tell You
Brain damage patients with anosognosia are incapable of considering, noticing, admitting, or realizing even after being argued with, that their left arm, left leg, or left side of the body, is paralyzed. Again I'll quote Yvain's summary:
A brief search didn't turn up a base-rate frequency in the population for left-arm paralysis with anosognosia, but let's say the base rate is 1 in 10,000,000 individuals (so around 670 individuals worldwide).
Supposing this to be the prior, what is your estimated probability that your left arm is currently paralyzed?
Added: This interests me because it seems to be a special case of the same general issue discussed in The Modesty Argument and Robin's reply Sleepy Fools - when pathological minds roughly similar to yours update based on fabricated evidence to conclude they are not pathological, under what circumstances can you update on different-seeming evidence to conclude that you are not pathological?