The correct answer is:
$$P\left( {A/B} \right) = \frac{{P\left( A \right) \cdot P\left( {B/A} \right)}}{{P\left( B \right)}}$$
This is the conditional probability formula. It tells us that the probability of event A happening given that event B has already happened is equal to the probability of both events happening divided by the probability of event B happening.
In other words, if we know that event B has happened, then the probability of event A happening is increased or decreased depending on how likely event A is to happen given that event B has already happened.
For example, let’s say that we are flipping a coin. The probability of flipping heads is $\frac{1}{2}$. Let’s also say that we know that the coin has landed on heads on the last 10 flips. The probability of flipping heads on the next flip is still $\frac{1}{2}$, but the conditional probability of flipping heads given that the last 10 flips were heads is much higher than $\frac{1}{2}$. This is because we know that the coin is more likely to land on heads than tails after 10 consecutive heads.
The conditional probability formula can be used to calculate the probability of any event given that another event has already happened. It is a powerful tool that can be used to make predictions about the future.
The other options are incorrect because they do not take into account the probability of event B happening. Option A is the probability of event A happening, but it does not take into account the fact that event B has already happened. Option B is the probability of both events happening, but it does not take into account the probability of event B happening. Option C is the probability of event B happening, but it does not take into account the probability of event A happening.