Suppose you have to choose between, on the one hand, a P1 probability of C happening vs. a (1 - P1) probability of some baseline B happening, like a 90% probability of getting a Cherry, say; or on the other hand, a P2 probability of D happening vs. (1 - P2) of B, like a 80% probability of getting a Date. We could say that Preference(0.9, Cherry, Baseline) is how much you desire that gamble over those two outcomes; and Preference(0.8, Date, Baseline) is how much you want the other. If a switch controls which of those two you get, then the gamble to which you attach the higher Preference is the one you'll want the switch to be thrown for.
Now suppose that, in the composition of Events as pathways through Time, there is interposed some new event with probability P3 that determines whether the switch is run at all; if not, the outcome is Baseline.
The condition for not throwing the switch and then throwing it back, is that if Preference(0.9, Cherry, Baseline) > Preference(0.8, Date, Baseline), then Preference(0.9*P3, Cherry, Baseline) > Preference(0.8*P3, Date, Baseline), likewise if the value is equal, or lesser. Combine this with simpler ideas like "If you prefer 100% of one thing to 100% of another, you should prefer higher probabilities of getting that thing rather than the other, in gambles between them" and you can pretty thoroughly spotlight the Law of Probable Utility showing that Preference() must compound probabilities with utilities the same way that independent probabilities compound with each other. So, yes, multiplication.