You Win?

You are a winner of a lottery! However, you may not be the only winner. The number of other people who won the lottery is $N \sim \text{Poisson}(\lambda)$, where $\lambda > 0$ is a constant. Given $N = n$, the person who actually receives all the money is randomly selected from the $n+1$ total winners (you and the other $n$ people). Find the probability that you actually receive the money when $\lambda = 1$, rounded to the nearest thousandth.