White to move! Win, lose or draw?
In essence, when the pawn is on b5, white can threaten to win the backward pawn by allowing black to queen the g-pawn, and then force the exchange of queens or the queen for the remaining pawn- black defeats this plan in the position diagrammed above by advancing the h-pawn in the critical line and queening that one instead, but at the cost of blocking the g-pawn- when the white pawn is on b5, though, this cost black a critical tempo.
Dogeval is correct, this is a theoretical draw. Interestingly, white can win if the pawn were on b5 rather than b4- white then has the time to get his second queen on the board before black can queen his second pawn (the king is on g1 at the critical juncture. I had to go to the Nalimov Tablebase to see this- this ending is quite complicated as are many Q and P endings.