Knight Probability - The Setup

The knight's position matters. A knight in the center has all 8 moves available. A knight in a corner might have only 2 legal moves (the rest go off-board). The number of remaining moves matters too.

With $k=0$ moves left, if you're on the board, probability is $1$. With $k=1$, it depends on how many of your 8 moves stay on-board. State: $(row, col, moves\_left)$. Value: probability of staying on-board from this state to the end.