You wouldn't necessarily end up with a single reality, but if there was some kind of process "sampling" a finite number of realities from the wavefunction (eith

You wouldn't necessarily end up with a single reality, but if there was some kind of process "sampling" a finite number of realities from the wavefunction (either continuously, e.g. if quantum collapse is ontic, or e.g. at some time in the distant future god takes a look at the state of the wavefunction) where the sample probability was calculated in the normal way (square of the wavefunction magnitude), that would explain how probability "gets into" quantum mechanics. This is kind of an open question, though - you can find plenty of papers (mostly bad) wondering out loud how you get the appearance of "discrete" realities with things like probability when quantum mechanics appears to be continuous.