This isn't intended as a full discussion, I'm just a little fuzzy on how a Bayesian update or any other kind of probability update would work in this situation.

You have a coin with a 99.9999% chance of coming up tails, and a 100% chance of coming up either tails or heads.

You've deduced these odds by studying the weight of the coin. You are 99% confident of your results. You have not yet flipped it.

You have no other information before flipping the coin.

You flip the coin once. It comes up heads.

How would you update your probability estimates?

(this isn't a homework assignment; rather I was discussing with someone how strong the anthropic principle is. Unfortunately my mathematic abilities can't quite comprehend how to assemble this into any form I can work with.)