continue to believe that the probability that the coin is fair is $0$. If that is not your prior opinion, you should not use this beta prior (even though its mathematical properties are convenient). Also, Bayes' Theorem states that: $$P(X=x|D=d) = \frac{P(X=x)P(D=d|X=x)}{P(D=d)}$$ Let $D$ represent your data. You usually know $P(D=d|X=x)$,