I don't think physicists actually have the right answer when they do that. You can use Feynman path integrals for quantum physics, and it will get the right answer if you cheat like that, but I'd bet that it's actually more related to linear equations, which don't require cheating.

Physicists use renormalization and cutoff techniques. The universe doesn't.

Also, Pascal's mugging seems to be looking at a special case where it does converge. If you actually used Solomonoff induction, it wouldn't converge because of the possibility of this sort of thing, whether or not someone ever actually makes a threat.