Conditional probability Given the events $A, B$ the conditional probability of $A$ supposing that $B$ happened is:
$$P(A | B)=\frac{P(A\cap B )}{P(B)}$$
Can we write that for the Events $A,B,C$, the following is true?
$$P(A | B\cap C)=\frac{P(A\cap B\cap C )}{P(B\cap C)}$$
I have couple of problems with the equation above; it doesn't always fit my logical solutions.
If it's not true, I'll be happy to hear why.
Thank you.

Yes you can. I see no fault. Because if you put $K = B \cap C$ you obtain the original result
