I do not understand how
P(A|B,C)=P(A|C)
is derived from
P(A∩B|C)=P(A|C)P(B|C)
on this site.
I'm stuck on the statement:
By conditioning on C, we obtain P(A|B,C)=P(A∩B|C)/P(B|C)
Should the left hand side of the equation be P(A|B|C)?
Update
From this site:
Definition
Two events A and B are conditionally independent given an event C with P(C)>0 if
P(A ∩ B | C)=P(A | C) P(B | C) equation (1.8)
Recall that from the definition of conditional probability,
P(A | B) = P(A ∩ B) P(B),
if P(B)>0. By conditioning on C, we obtain
P(A | B , C) = P(A ∩ B | C) P(B | C)
How is this last equation P(A | B , C)= P(A ∩ B | C) P(B | C) derived? What does it mean to condition on C?