Suppose you say that you’re 99.99% confident that 2 + 2 = 4.

Then you're a dillbrain.

Then you have just asserted that you could make 10,000 independent statements, in which you repose equal confidence, and be wrong, on average, around once. Maybe for 2 + 2 = 4 this extraordinary degree of confidence would be possible

Yes, how extraordinary that I can say every day that the guy in front of me at the bodega won't win the Powerball. Or that [SystemRandom().random() >= 0.9999 for i in range(10000)] makes a list that is False in all but one spot.

P(x|y) is defined as P(x,y)/P(y). P(A|A) is defined as P(A,A)/P(A) = P(A)/P(A) = 1. The ratio of these two probabilities may be 1, but I deny that there's any actual probability that's equal to 1. P(|) is a mere notational convenience, nothing more.

No, you kneebiter.