Conditional probability question?

Question

My books says the equation for a conditional probability is
p(A/B)=p(AnB)/p(B). Does this mean that it works the opposite way to, for example p(B/A)=p(BnA)/p(A) or does it not change. Also I have a book question that when answer the equation was
p(B/A)=p(AnB)/p(A) how does that work, i thought there was a set equation and it was always either p(AnB)/p(B) or p(BnA)/p(A). In what circumstances do you get p(AnB)/p(A)?

Answer 1

My books says the equation for a conditional probability is
p(A/B)=p(AnB)/p(B).
Does this mean that it works the opposite way to, for example p(B/A)=p(BnA)/p(A) or does it not change.

Yes it works the opposite way to

Also I have a book question that when answer the equation was p(B/A)=p(AnB)/p(A) how does that work, i thought there was a set equation and it was always either p(AnB)/p(B) or p(BnA)/p(A). In what circumstances do you get p(AnB)/p(A)?

This come from the following

p(BnA)= p(AnB)

Let say B is for being old and A for being a girl
p(BnA) is the probability to be old and a girl
p(AnB) is the probability to be a girl and old
it’s the same

Answer 2

A and B are symbols and can be interchange in the formula. Also p(AnB) = p(BnA)