Knight Probability - State Definition

Define $dp[r][c][k]$ = the probability that a knight starting at $(r, c)$ with $k$ moves remaining stays on the board for all $k$ moves. The answer we want is $dp[row][col][K]$ where $(row, col)$ is the starting position and $K$ is the total number of moves.

Why this state? It captures everything that matters: where you are and how many moves are left. Given your current position and remaining moves, the future probability depends only on these values, not on the path you took to get here (Markov property).