fredthebear: In the final position, Black appears to be OK after the forking move 42...Kb3. But White should not try to defend his backward b-pawn. (The defensive 43.Kc1 would result in a draw, a blunder on White's part.)
Rather White gains the opposition of kings to put Black in zugzwang. After 42...Kb3 43.Kd3 is the proper reply. It does not matter which pawn Black captures now, for White responds the same to either capture with 44.Kc4 getting the upper hand. Black can have either the a-pawn or the b-pawn, but not both and the Black king loses effectiveness on the edge. White will soon have a passed pawn on either side of the board, depending upon Black's responses. Thus...
43...Kxb2 44.Kc4 Ka3 45.Kb5 Kb3 46.Kxa5 Kc4 47.Kb6 (or 46...Ka3 47.Kb5) and White has a passed a-pawn that will promote.
43...Kxa4 44.Kc4 and the Black king finds himself "stalemated" on the queenside by the opposition, being forced to play the only moveable unit with 44...h6 or h5 to which White replies 45.gxh6 en passant with effortless promotion to follow. Yet beware! The pawn-takes-pawn on h6 also frees Black's g-pawn to move -- the only move available, so White can avoid a final stalemate as long as he does not remove the g-pawn. Now that White has a distant passed h-pawn, it would be wise to play the safe, simple Kc3 to avoid stalemate by allowing the Black king to harmlessly wander out backward. Now White can capture Black's g-pawn before it too promotes. The point is, capturing the Black g-pawn too soon would remove Black's only mobile unit and stalemate would be the result; Kc3 eliminates this possibility.
Once White promotes either outside pawn to queen, she will soon zoom in to deliver checkmate.
This is a good example of an endgame in which masters see the final outcome through to it's conclusion and resign. However, amateurs should continue to play and make their opponent prove the proper use of the opposition of kings and the avoidance of stalemate.