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 moves left, if you're on the board, probability is . With , it depends on how many of your 8 moves stay on-board. State: . Value: probability of staying on-board from this state to the end.