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.)