#additive-smoothing

A DAG over binary variables has $t \to s \leftarrow b$ and $t \to x$. Among ten iid fully observed records, exactly three have $t = 0, b = 0$, and all three of them have $s = 0$. Each entry of the table $p(s = 1 \mid t, b)$ gets an independent uniform prior on $(0, 1)$. What is the posterior mean of $p(s = 1 \mid t = 0, b = 0)$?