Three balls are randomly and independently tossed into bins numbered with the positive integers so that for each ball, the probability that it is tossed into bin $i$ is $3^{-i}$ for $i=1,2,3,\dots$. More than one ball is allowed in each bin. The probability that the balls end up in three consecutive distinct bins (e.g., bins $k,k+1,k+2$) is $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. What is $p+q$?