The Enigma of Existential Probability

In the realm of quantum mechanics, where uncertainty prevails, consider a hypothetical experiment involving a particle whose precise position and momentum are unknown. The particle is confined within a sealed chamber, and a measurement is performed to determine its position with utmost precision. Subsequently, a measurement is taken to ascertain its momentum. Now, if these measurements were repeated numerous times, each time with the position or momentum being randomly determined, what is the fundamental limitation or constraint that emerges, reflecting the intrinsic nature of reality?