LeetCode 808 Soup Servings - State Definition

After scaling by $25$, define $dp[a][b]$ = probability that A empties first (plus half of both empty) given $a$ units of A and $b$ units of B remain. Base cases:

$1.$ If $a \leq 0$ and $b \leq 0$: both empty simultaneously. Return $0.5$.

$2.$ If $a \leq 0$: A emptied first. Return $1$.

$3.$ If $b \leq 0$: B emptied first. Return $0$. The answer is $dp[n/25][n/25]$, rounded up if not divisible. This dp definition has all the information needed to compute the probability from (a, b).