Phil is right, and also “don’t believe him” is a mapping of “the thing he said is x% likely” onto a single believe/don’t with a cutoff at t%. So it can be true that both
A) you update to believe it is more than 1⁄1,000,000 that Xavier won, but also
B) your level still falls below t%, so you don’t believe it.
As I’ve noted before, this is actually how real people behave. They know the odds of winning are super low, so when they get a bit of evidence that says “I won” they seek out independent bits of evidence (eg, asking a second person to look at the ticket and confirm the numbers; checking their bank account after putting in the claim to confirm the balance was updated) before acting on the reality of winning.
Phil is right, and also “don’t believe him” is a mapping of “the thing he said is x% likely” onto a single believe/don’t with a cutoff at t%. So it can be true that both A) you update to believe it is more than 1⁄1,000,000 that Xavier won, but also B) your level still falls below t%, so you don’t believe it.
As I’ve noted before, this is actually how real people behave. They know the odds of winning are super low, so when they get a bit of evidence that says “I won” they seek out independent bits of evidence (eg, asking a second person to look at the ticket and confirm the numbers; checking their bank account after putting in the claim to confirm the balance was updated) before acting on the reality of winning.