If agnosognosics by definition place a probability of zero on their arm being paralyzed, and thus on being agnosognosics...
I'm kicking myself for not realizing this, but you're right. A probability of zero on their left arm being paralyzed only comes from people with anosognosia and people who are not paralyzed. Therefore, a non-zero probability only comes from people who are paralyzed and do not have anosognosia, in which case their probability is 1.
Estimating between zero and 1 by definition means you cannot be anosognosic. However, it also means you are not paralyzed, because only anosognosic paralytics place a non-1 probability on their condition. Therefore, if you are not certain you are paralyzed, you must be certain you are not. I am subsequently forced to place a probability of zero on my left arm being currently paralyzed.
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?