Entropy $\mathcal{H}(\pi)$ of a distribution over $|\mathcal{A}|$ actions

$\pi$ puts probability $p$ on one action, distributes $1-p$ uniformly over the remaining $|\mathcal{A}|-1$

$\mathcal{H}(\pi) = \underbrace{-p\log p}_{\color{#2563eb}{\text{from action 1}}} \underbrace{- (1-p)\log\frac{1-p}{|\mathcal{A}|-1}}_{\color{#dc2626}{\text{from remaining }|\mathcal{A}|-1\text{ actions}}}$