One could model this as “there are infinite claims with 0 evidence, so given any finite resource X, I should spread that X evenly over all infinite claims—therefor I am willing to spend at most epsilon resources on any given cause.” Given that listening to the person STATE the claim is WELL above epsilon resources, one has already over-invested, and can safely move on to the next infinitesimally unlikely claim.
One could model this as “there are infinite claims with 0 evidence, so given any finite resource X, I should spread that X evenly over all infinite claims—therefor I am willing to spend at most epsilon resources on any given cause.” Given that listening to the person STATE the claim is WELL above epsilon resources, one has already over-invested, and can safely move on to the next infinitesimally unlikely claim.