A uniform distribution is where the probabilities are evenly distributed across the sample space. $$ p(s_i) = \frac{1}{n} \text{ for all } i = 1 \text{ to } n $$
title: Example
Given the uniform distribution on $S$.
If a fair dice is rolled, then there are six possible equally likely outcomes: $1,2,3,4,5,6$.
So $p(1) = p(2) = ... = p(6) = \frac{1}{6}$.