Mail Time

You got mail! A letter is going to be sent to one of $N \geq 2$ mailboxes (labelled $1-N$) uniformly at random. If the mail ends up in mailbox $i$, there is a probability $p_i$ that you actually read the mail. Given that you checked mailbox $1$ and you didn't read a letter, find the probability that the mail was actually sent to mailbox $1$. Report the answer when $N = 10$ and $p_i = 1-\frac{i}{10}$ for $1 \leq i \leq 10$.