Suppose there are three events then which formula must always be equal to P(E1|E2,E3)?

This is an application of conditional probability: P(E1,E2)=P(E1|E2)P(E2). so

P(E1|E2) = P(E1.E2)/P(E2)

P(E1,E2,E3)/P(E2,E3)

If the events are A and B respectively, this is said to be "the probability of A given B"

It is commonly denoted by P(A|B): or sometimes PB(A). In case that both "A" and "B" are categorical variables, conditional probability table is typically used to represent the conditional probability.