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When the Queen is placed, it becomes Black's turn. Black is not in check, but is in a situation where there are no legal moves for Black to play (his pawns cannot advance, and the king has no legal squares to land on. Because of this, Black can claim a draw instead of a loss.

Promoting to a queen would result in a stalemate as the black player would have no legal moves. Promoting to a bishop allows the king to move to the the 8th row, allowing the final checkmate by white

If white promotes to a queen, black will have no legal moves because the king can't move into check, and the pawns can't move at all. If a player can't move, the game is a draw.