Alice and Bob and the referee Conny play the following game with a pawn on a standard $8\times8$ chessboard:
- In the beginning, Conny places the pawn into the center of a randomly chosen square. All $64$ squares are chosen with equal probabilities.
- Then Alice and Bob alternate turns; Alice starts.
- In every turn, the pawn is moved to a new square. The pawn is always placed into the very center of a square.
- The (Euclidean straight line) distance moved by the pawn must be strictly larger than the (Euclidean straight line) distance moved by the pawn in any of the preceding moves.
- A player unable to move loses the game.
Question: What is the probability that Alice wins this game? (As usual, we assume that Alice and Bob both use optimal strategies.)