Interestingly, Black is much better off with one less pawn. In the first position, he simply plays 1.Kc4 and 2.Kb5 which forces the knight to give up its protection of the White pawn. Once White's pawn is gone, the position is drawn.
In the second position, Black is dead lost because his pawn prevents his King from reaching a square from which it can attack both the knight and the pawn. After 1...Kc6 2.Kh4 Kb6, the White knight moves to safety with 3.Nc5. Now it will take three moves for the Black king to attack the White pawn, 3...Kc6, 4...Kd5, and 5...Kc4, whereupon the White knight protects the pawn with Na6, when it will take the Black king another three moves to get back to b6. White can use this time to pick off the Black h-pawn after which it comes over to gang up on the Black b-pawn.
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