$$ P(H|E) = \frac{P(E|H) * P(H)}{P(E)} = \frac{P(E|H) * P(H)}{P(E|H) * P(H) + P(E|\neg H) * P(\neg H)} $$
$$ \text{posterior of H given the evidence} = \frac{\text{likelihood of E if H is true} * \text{prior prob}}{\text{priori prob evidence itself is true}} $$