Well, you'd need a method of handling infinite values in your calculations. Some methods exist, such as taking limits of finite cases (though much care needs to be taken), using a number system like the Hyperreals or the Surreals if appropriate, or comparing infinite cardinals, it would depend a little on the details of how such an infinite threat was made plausible. I think in most cases my argument about the threat being dominated by other factors would not hold in this case.

While my point about specific other actions dominating may not hold in this case, I think the overall point that infinite resources cause problems far more fundamental than the mugging is if anything strengthened by your example. As is the general point that large numbers on their own are not the problem.