I wasn't expecting that .......

Suppose we have $8$ distinct containers and $8$ indistinguishable balls. The balls are then distributed into the containers such that the distribution is uniform across all possible events. That is, each distribution $(a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7},a_{8})$ of balls, where $a_{n}$ is the number of indistinguishable balls in the $n$th container such that $\sum_{n=1}^8 a_{n} = 8$, is equally likely to occur.

The expected number of containers that have at least one ball in them is $\frac{a}{b}$, where $a$ and $b$ are positive coprime integers. Find $a + b$.