From the sample space sequals={1, 2, 3, 15} a single number is to be selected at random. given event a, that the selected number is even, and event b, that the selected number is a multiple of 4, find p(upper a vertial line upper ba∣b).

Given
E={1,2,3,4,514,15}   sample space
A={2,4,6,...14}  even numbers
B={4,8,12}  multiples of 4
To find: P(A|B)

We deduce from above that 
P(A)=7/15
P(B)=3/15
P(A ∩ B)=3/15  since B is a subset of A.

The conditional probability P(A|B) is the probability of A happening given B has already happened.  
So if a number has been selected, and it is known that B has happened, (i.e. multiple of 4), we know that there is a 100% probability A has happened (even).

Mathematically, P(A|B) is defined as P(A ∩ B)/P(B).
So 
P(A|B)
=P(A ∩ B)/P(B)
=(3/15)/(3/15)
=1   (as reasoned above).

P(A|B)=1