Let $\{x_0,x_1\}$ be to states. Suppose the reward is $1$ in state $x_1$, and in state $x_0$ it is $1$ with probability $r$ and $0$ with probability $1-r$, with $r\in(0,1)$.
Bob has a belief $p\in [0,1]$ over the states $x_0$ and $x_1$, i.e., $p$ is the probability that the true state is $x_1$ according Bob.
Suppose the true state is $x_0$. If $p\in[0,1)$ and Bob observes a reward of $0$, he updates his belief according to Bayes' rule and is new belief is $0$.
Suppose now that $p=1$, that is Bob is sure that the true state is $x_1$ when it is actually $x_0$, and suppose the Bob observes a reward of $0$.
Bayes' rule in this case would give "$\frac{0}{0}$".
My question is, Bob being Bayesian, will his new belief be $0$ or $1$, and why?