Mathematics

The normalization axiom captures the idea that probability measures the certainty of all possible outcomes combined—there's nowhere else for probability to "go." Since one of the outcomes in your sample space $S$ must occur, the total probability assigned to $S$ must equal 1. This axiom ensures probabilities are calibrated on a meaningful scale: 0 means impossible, 1 means certain, and everything in between is proportional likelihood.

The normalization axiom captures the idea that probability measures the certainty of all possible outcomes combined—there's nowhere else for probability to "go." Since one of the outcomes in your sample space $S$ must occur, the total probability assigned to $S$ must equal 1. This axiom ensures probabilities are calibrated on a meaningful scale: 0 means impossible, 1 means certain, and everything in between is proportional likelihood.