Empirical probability distribution ($\hat{p}(x)=n^{-1}{\sum }_{i=1}^n{1}_{\{x_i=x\}}$)

For a nonempty finite sample, assign each distinct observed value its relative frequency. The observed values form the finite positive-mass support; the counts sum to the sample size, so the probabilities sum to one. Repeated observations increase the same outcome's mass rather than adding repeated support entries.