To find the complement of $P(A)$, we need to calculate $P(\overline{A})$, which represents the probability that event $A$ does not occur. The formula for the complement is:

$P(\overline{A}) = 1 - P(A)$

Given that $P(A) = \frac{1}{13}$, we can substitute:

$P(\overline{A}) = 1 - \frac{1}{13} = \frac{13 - 1}{13} = \frac{12}{13}$

So, the answer is:

$P(\overline{A}) = \frac{12}{13}$

Let me know if you need further explanation!

Here are some related questions:

1. What does it mean for two events to be complements?
2. How would you calculate the complement if $P(A)$ was a decimal?
3. Can the complement of an event ever be greater than 1?
4. How does the probability of the complement change if $P(A)$ increases?
5. What is the sum of $P(A)$ and $P(\overline{A})$ for any event $A$?

Tip: The probability of an event and its complement will always add up to 1.