Earlier quoted context omitted.
The problem is, then white queen follows up with checks which eventually also attack the black pawn. Since the black pawn is at a3, there is no immediate threat of queening. If black moves the king away from the pawn, white grabs it. If black keeps the king near the pawn, white forces black king under the pawn, and then moves his king, and black is forced to give up the pawn. Every continuation is losing for black.
The black pawn is on the h-file and never goes to a3. It's on h2 at the point where White queens with check. Black plays Kg1 and reaches a well known drawing position [0]. This is one of the first chess endgames most people learn after how to mate with queen or rook. Like I said, anyone playing at more than a beginner level normally knows this. Kf2 (instead of Kg2) draws in the same way. [0] https://en.wikipedia.org/…
Meant h3, sorry, result of mental calculations.
I just checked on an analysis engine, and it confirms: every position is losing for black, as long as white does not mess it up, and has the first move.
You can try it out here: https://www.chess.com/analysis
Load FEN: 8/2K5/8/7p/P7/5k2/8/8 w - - 0 1