 Borel–Kolmogorov paradox

The Borel–Kolmogorov paradox arises in the context of probability theory, specifically dealing with the issues that can arise when a seemingly intuitive approach to probability is applied to certain continuous distributions. The paradox highlights how different ways of defining conditional probabilities can lead to contradictory or counterintuitive results. To explain the paradox, consider the following scenario: 1. **Setup**: Imagine a perfectly random process that produces real numbers uniformly in the interval [0, 1].