The legendary Indian national hero Sid has $3$ boxes. He also regularly receives gifts from his many fans. When he receives a gift, he randomly places it in one of his $3$ boxes. Sid has received $10$ gifts so far. The expected value of the number of empty boxes can be expressed in the form $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $a+b$.