Borel's paradox

Borel's paradox involves the surprising outcome that, in probability theory, conditioning on an event of zero probability can lead to different, conflicting results depending on how the event is described or approached. Imagine trying to update beliefs based on an exact point—like specifying an exact longitude on Earth. Different reasonable methods of "zooming in" on that point can lead to different conclusions about the probability of another event. This paradox highlights that conditioning on events with zero probability isn't straightforward and requires careful mathematical treatment to avoid inconsistencies.