You Got Mail

A letter is going to be sent to one of three mailboxes uniformly at random. These mailboxes are labelled $1-3$. If the mail ends up in mailbox $i$, then there is a $\dfrac{i}{3}$ probability that the mail is actually read. Given that you checked Mailbox $1$ and didn't read any letter, find the probability that the mail ended up in Mailbox $1$.