I would probably assign the same value I do to other very implausible religious claims.

Here's an example of rounding down to zero, leading to bad EV results. Imagine your eccentric uncle dies. He gives a sealed box to John and to a trillion other people. He told you that he flipped a coin- if it was heads, he put all his 1 million dollar fortune in John's box. If tails, he put it in someone else's box. You assume that the probability it's in John's box is 0.5 and the probability for each other box is 1 in 2 trillion. If it was tails, you're not sure how he chose what box to put it in. If you could talk to his widow you might gain valuable information- perhaps he put in the box of neighbor. The probability for each box other than John's is low and very uncertain. You round down the probability for each other box to zero. Since probabilities add up to 1, you're confident that John's box has a million dollars. You offer to but it from him for $950K. But that's absurd.