Conditional probability and probability updating

The conditional probability formula is supposed to reflect the correct updating of probability assignments when new information is incorporated. Starting from a non-atomic probability measure, it is proved that the conditional probability formula provides the only transformed probability measure satisfying a minimum requirement relational assumption. This result applies to the standard Bayesian parametric model.

Automated summary

The conditional probability formula accurately updates probability assignments when new information is added. It is proven that this formula is the only transformed probability measure that satisfies the minimum requirement relational assumption, using a non-atomic probability measure. This result is applicable to the standard Bayesian parametric model.