The probability that every child would have strictly more of a candy than each other trick-or-treater was precisely 318281087/8016470462, which comes to just under 4%. The most straightforward way to compute this was to assign a particular candy to each child and compute the probability of that (writing some code certainly helped here) and then multiplying the result by 120 to account for the disjoint other assignments of candy to trick-or-treater.

Congrats to the following solvers who managed to submit the precise probability correctly!