Entropy bound with one prescribed probability
= Entropy bound with one prescribed probability
{title2=$H\leq h(t)+(1-t)\log_2(k-1)$}
If one probability in a $k$-point distribution equals $t$, normalize the remaining $k-1$ probabilities to $q$. Then $H=h(t)+(1-t)H(q)\leq h(t)+(1-t)\log_2(k-1)$. Equality for $t<1$ means that the remaining probabilities are equal. This combines the <binary entropy> of the distinguished event with the largest residual <Shannon entropy>.