1. P(A|B)=P(A,B)/P(B) (the comma represents intersection)

2. P(A1,A2,...,An)=P(A1)P(A2|A1)...P(An|A1,A2,...An-1)

3. P(A|B)=[P(B|A)P(A)]/P(B) (Bayes' Rule)

I'm curious about conditioning with more than one event:

P(B|A1,A2,...,An) for n events.

In particular, I don't know the stipulations for the A1,A2,...,An

As I understand conditional probability, I am updating prior probability with the evidence I collect. Can someone give me a formal definition for conditioning with more than one event and some working theorems?