A frequent application of conditional probability is where we are given a bunch of just information, so in this case what we're looking at is probability of a and b is 1/4 probability of b given a is 2/3 and we are asked to find the probability of a.
For something like this, all we have to do is plug it into our relationship. We have a formula for conditional probability, all we need to do is plug in the data and solve for the thing we're looking for.
So probability of b given a is 2/3 is equal to probability of a and b 1/4 divided by probability of a, solve this out all we have to do is multiply both sides by probability of a so we end up with 2/3 probability of a is equal to 1/4, multiply both sides by 3/2 and we end up with the probability of a is equal to that's a 3/2 isn't it? 3/2 probability of a is equal to 3 over 8.
So a simple application of conditional probability, take what they give you, plug into the formula and solve accordingly.