Now that we know how to imagine a cardon square, we see that the Black King is well within the cardon squares of both pawns.
1.Kf4
Kxb3
Though the Black King has grabbed a free Pawn, he has stepped outside the cardon square of the other pawn. Now it is White's turn to move as well.
2.a5
Imagine a new cardon square from the new position of this Pawn.
2...Kb4
3.a6
As the cardon square is getting smaller and smaller every move, Black King will never be able to catch up.
3...Kb5
4.a7
Kb6
5.a8Q
And wins. *