Don't update your priors on the basis of unreliable sources. If someone walks up to you and says "This is a fair coin, and the odds of it coming up heads the next 100 times in a row are 1/2^20, provided it is flipped 100 times in a row.", you don't update based on that, at all. That statement does not make a run of heads more or less likely.

Similarly, when someone makes a claim about magical falling ponies, I don't update my estimate of the odds of magical flying ponies unless their claim is credible.

As a check- I say that the (fair) coin nearest to you will turn up heads the next 100 times it is flipped, as of the time you read this. Do you think the odds of that happening are greater, less than, or exactly equal to 1/2^100? Did you update your estimate based on my claim? Why or why not?

(You could suggest that the odds of a particular post being by Omega, who has specific unexplainable knowledge about the future, are sigma, and so the odds are 1/2^100+sigma. Now compare that with the odds that a particular post is by Omega, and that he is lying. That makes the odds 1/2^100 + sigma - sigma; the odds provided that neither alternative is true, plus the odds that all-heads will be forced, plus the odds that not-all-heads will be forced. Which sigma is greater, or are they exactly equal? On what basis do you judge that?)