One random number strictly topping another

Jimmy picks a number uniformly at random from $\{1,\dots,1000\}$ and, independently, Simon picks one uniformly from $\{1,\dots,3000\}$. What is the probability that Simon's number is strictly greater than Jimmy's?

$4999/6000$. Given Jimmy picks $k$, Simon beats it with probability $\tfrac{3000-k}{3000}$. Averaging over $k$: $1-\tfrac{1}{3000}\cdot\tfrac{1001}{2}=1-\tfrac{1001}{6000}=\tfrac{4999}{6000}$.