Knight Probability in Chessboard LeetCode solution in Python

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class Solution:
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    def knightProbability(self, n: int, k: int, row: int, column: int) -> float:
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        x_dir = [2, 1, -1, -2, -2, -1, 1, 2]
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        y_dir = [1, 2, 2, 1, -1, -2, -2, -1]
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        cache = {}
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        def kMoves(i, j, moves):
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            if i >= n or j >= n or i < 0 or j < 0:
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                return 0
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            if moves == k:
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                return 1
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            if (i, j, moves) in cache:
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                return cache[(i, j, moves)]
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            totMoves = 0
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            for ind in range(8):
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                totMoves += kMoves(i + x_dir[ind], j + y_dir[ind], moves + 1) * (1 / 8)
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            cache[(i, j, moves)] = totMoves
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            return totMoves
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        return kMoves(row, column, 0)