I was just looking into a Bayesian model for flipping a coin. Let $\theta$ denote the bias of the coin. A bias of $1$ will always land on heads $h$ and $0$ will aleays land on tails $t$. It was said that a good candidate for the likelihood is the binomial distribution $$p(h\mid\theta) = \frac{n!}{h!(n - h)!}\theta^h(1 - \theta)^{(n-h)}$$
But then I noticed... If I were to set $\theta = 1$ then this gives $$\frac{n!}{h!(n - h)!}\cdot 1^h\cdot(1 - 1)^{(n-h)} = 0$$
So that means that the probability of getting heads, given the bias is $1$ is zero? I am very confused by this. How can this be?