Conditional probability is denoted as P(A|B)=Probability of occurrence of A when B occurs OR Probability of Event A when B becomes a sample space.
Let us take an example:Let there be 5 white and 4 red balls.Two balls are drawn from the bag one after another without replacement. If we consider these events:
A= Drawing a white ball in first draw
B= Drawing a red ball in second draw.
P(B|A)= Probability of drawing a red ball from a bag containing 4 white and 4 red balls.
Here I fail to understand how event A can be considered the sample space for the given conditional probability.The sample space for Event A is just white balls while that of this probability is : total number of balls-one white ball from event B.Also what is the intuition behind considering Event A as a sample space if it is?