From the sample space $S=\{1,2,3,4, \ldots, 15\}$ a single number is to be selected at random. Given the following events, find the indicated probability.
A: The selected number is even.
$B$ : The selected number is a multiple of 4. .
$C$ : The selected number is a prime number.
$P(A \mid B)$
$P(A \mid B)=\square$ (Simplify your answer. Type an integer or a fraction.)

Step 1 ：From the sample space $S=\{1,2,3,4, \ldots, 15\}$ a single number is to be selected at random. Given the following events, find the indicated probability.

Step 2 ：A: The selected number is even.

Step 3 ：$B$ : The selected number is a multiple of 4.

Step 4 ：$C$ : The selected number is a prime number.

Step 5 ：We are asked to find $P(A \mid B)$, the conditional probability of event A (the selected number is even) given that event B (the selected number is a multiple of 4) has occurred.

Step 6 ：In other words, we want to find the probability that the selected number is even, given that we know it is a multiple of 4.

Step 7 ：Since all multiples of 4 are even, if we know that the selected number is a multiple of 4, we can be certain that it is also even. Therefore, the probability of event A given event B is 1.

Step 8 ：Final Answer: $P(A \mid B)=\boxed{1}$