What does it mean for a measurement to be probabilistic? I'm a math grad student, so still a layman, but here's the way I think about it: Every particle travel

What does it mean for a measurement to be probabilistic? I'm a math grad student, so still a layman, but here's the way I think about it: Every particle travels over every possible path as the wave spreads out. Once you measure the particle, it tells you a path. So the measured value of the particle is probabilistic, not the measurement.