You CAN'T ignore the extra information like P(Rain|Seattle) though. What if this were the question instead: "Three friends in Seattle told you that Earth explo

You CAN'T ignore the extra information like P(Rain|Seattle) though. What if this were the question instead: "Three friends in Seattle told you that Earth exploded and everyone died. Each has a probability of 1/3 of lying. What’s the probability that the Earth exploded and everyone died?"