For example, in Pascal's Mugging, a random person threatens to take away a zillion units of utility if you don't pay them $5. The probability they can make good on their threat is miniscule, but by multiplying out by the size of the threat, it still ought to motivate you to give the money.

Why? Hasn't this been gone over before? Tiny number * big number = not determined by the words "tiny" and "big".