Suppose that you have to guess
the suit of a playing card drawn
from a 
pack at random,
you probability of guessing
correctly is 
.
Now suppose I tell you that it is red.
You then have a 
chance, because there
are less choices, you can use the additional information
to restrict the space of possible outcomes.
We write the probability of A given that A happened
as the probability of A given B: 
.
Definition of the conditional probability
of 
given 
:
