Why P(E|H) equal to L(H|E) in Bayes's rule? In the following Bayes's rule,
$$
P(H|E)=\frac{P(E|H)\cdot P(H)}{P(E)} 
$$
Many resources such as Wikipedia deduce that the probability of E given H equal to the likelihood of H given E or $P(E|H) = L(H|E)$.
I wonder why it is so? From my understanding the $P(E|H)$ is the distribution of E given H while $L(H|E)$ is the distribution of H given E. Why the distribution of different variable is equal to each other?
Thank you in advance for every answers!

$P(E|H)$is what you mentioned the distribution of $E$ given $H$.
The likelihood is the same distribution $P(E|H)$ but viewed as function of the variable $H$, i.e. you want to check how the $P(E|H)$ changes as you change $H$, in order to find the most probable $H$ that generated the data. That's why you can write $P(E|H)= L(H|E)$.
