Conditional Probability Help

Hello everyone. I was hoping I could ask for a little help with implementation of the conditional probability formula. To start, I know nothing or very little about stats so my notation and ability to write smart about this is a little on the embarrassing side.....

But first, let me provide you the use case. I am writing a paper in which I want to know the probability of something (A): A contains about 3 possible outcomes and I'll container those into a variable I assign (h).
A is likely to occur given B, which also contains items (evidence) which I assigned as (v).

My question: I know that conditional probability is denoted as P = (A|B) - but it seems too simple as I don't know how it contains (E) with A or B events (h or v). Do I need to consider the actual events (h or v) in the P(A|B) equation or just leave it as is?

So, I expect to be able to do this - determine that A (one or more of 4 actions) will occur given that B (one more events) has occurred.

I standby by to clarify or answer any questions.

My approach, if using the P = (A|B) approach was simply to find % of times the elements of A happened, the % of times elements of B happened, figuring P=(AnB) and then solving - something like P = (A|B) = P(AnB)/P(B)

Whew...that was messy. Thank you!!