It's completely counterintuitive, but that's how it works experimentally. For example:
Measure the spin of electrons in direction X (that's done with a weirdly shaped magnet). You'll get either +1 or -1 in a conveniently chosen unit system. That's already weird, you'll never measure +0.5 for example. Keep only the +1 electrons. You can measure them again and again, you'll always get +1 in the X direction.
Now measure those electrons in the Y direction, you'll also get either +1 or -1.
But now, if you measure in the X direction again, you'll get +1 or -1 with 50% probability; although before measuring in the Y direction, these electrons always had spin +1 in the X direction.
Oh I get that experiments prove out. What has always been unintuitive to me to the point of seeming wrong is that said spin is random and lives in a probability cloud that is probabilistic only until we observe it.
The math works and the experiments work, but it feels like a broken clock situation. It happens to correlate well, but the understanding and models are missing something in the actual underlying physics that, if understood, would throw the whole randomness part out the window.