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Kingreaper comments on A Thought on Pascal's Mugging - Less Wrong
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A 1/3e22 probability means you believe there's a 1/3e22 chance of the event happening.
If you have, for example a 1/1e9 chance of finding evidence that increases that to 1/3e12, then you have a 1/1e9*1/3e12 chance of the event happening.
Which is 1/3e21.
So, in order to be consistent, you must believe that there is, at most, a 1/1e10 chance of you finding evidence that increases the probability to 1/3e12.
At which point, the probability of losing your rationality is obviously higher.
Yes. Yvain's 1 in 50 million example, on the other hand, is fine, because the probability went down. In a more extreme example, it could have had a 50-50 chance of going down to 0 (dropping by a factor infinity) as long as there had been a 50-50 chance of it doubling. Conservation of expected evidence.