Consider a r.v. $X$ that takes values in the set Ω = {1, 2, 3, · · · , N} with equal probability. Determine $P(X > m)$ and $P(X > m + k | X > m)$ for integers m, k where $1 ≤ m < N$ and $m + k ≤ N$.
According to my understanding, $P(X > m)$ is straightforward = $1-m/N$.
Also, I know $P(X > m + k | X > m)$ = $P(X > m + k \cap X > m) / P(X > m)$.
But how to calculate $P(X > m + k \cap X > m)$? Or any other way to directly estimate the conditional probability $P(X > m + k | X > m)$?