user17: 8/8/8/5kp1/p7/P4K2/1P6/8 b - - 0 1

White just played Kf3, thereby gaining the opposition.
If there were no queenside pawns, what is on the kingside would be a "book" draw. That's because the White king can maneuver himself into a stalemate position on his first rank.
But in this position, if the White king can't move, White has to move the b pawn to b3, or to b4 via b3. In either event, Black's a pawn takes it, queens, and wins for Black.
Or does it?

user3831: The position is definitely lost for white. 
You can convince yourself about this by checking in an endgame tablebase. White either has to allow the g-pawn promotion or let his king be "stalemated", forcing him to push the b-pawn and be checkmated soon thereafter.
[Title "Best play according to an endgame tablebase"] 
[fen "8/8/8/5kp1/p7/P4K2/1P6/8 b - - 0 1"]

1... g4+ 2. Kg3 Kg5 3. Kf2 Kf4 4. Ke1 g3 5. Ke2 Ke4 6. Kf1 Kf3 7. Ke1 g2 8. Kd2 g1=Q 9. Kc3 Qc5+ 10. Kd3 Qd5+ 11. Kc2 Ke4 12. b3 Qxb3+ 13. Kc1 Qa2 14. Kd1 Kd3 15. Ke1 Qe2# 0-1

Or...
[Title "Example scenario without g-pawn promotion"]
[fen "8/8/8/5kp1/p7/P4K2/1P6/8 b - - 0 1"]

1... g4+ 2. Kg3 Kg5 3. Kg2 Kf4 4. Kf2 g3+ 5. Kg2 Kg4 6. Kg1 Kf3 7. Kf1 g2+ 8. Kg1 Kg3 9. b3 {or b4; forced, since the king cannot move} axb3 10. a4 b2 11. a5 b1=Q# 0-1


user9030: Black wins.
Black has a distant passed pawn and Blacks pawns are more advanced. White is bound to defend against g-pawn, while Black can do anything with a and b pawns. And White cannot win a pawn race, because Black is more advanced.
[Event "Original Position"]
[Site ""]
[Date ""]
[Round ""]
[White ""]
[Black ""]
[Result "0-1"]
[FEN "8/8/8/5kp1/p7/P4K2/1P6/8 b - - 1 2"]
[Setup "1"]

2... g4+ 3. Kg3 { Option 1, defending against g-pawn, fails.}  ( 3. Ke3 { Option
2, counter attack on the other side, which fails also, because Blacks pawns are
more advanced, Black wins the race.}  3... Ke5 4. Kd3 Kf4 5. b4 axb3 6. a4 g3
7. a5 g2 8. a6 g1=Q ) 3... Kg5 4. Kg2 Kf4 5. Kf2 g3+ 6. Kg1 Kf3 7. Kf1 g2+ 8.
Kg1 Kg3 9. b4 axb3  

However, if Black wouldn't have a-pawn that advanced, White could catch Black and avoid promotion after dealing with g-pawn.
For example:
[Event "Queenside Pawns Shifted"]
[Site ""]
[Date ""]
[Round ""]
[White ""]
[Black ""]
[Result "1/2-1/2"]
[FEN "8/8/8/p4kp1/P7/1P3K2/8/8 b - - 1 3"]
[Setup "1"]

3... g4+ 4. Kg3 Kg5 ( 4... Ke5 5. Kxg4 Kd5 6. Kf4 Kc5 7. Ke5 ( 7. b4+ axb4 8.
Ke3 b3 9. Kd2 Kb4 10. Kc1 Kc4 11. Kb2 Kb4 12. a5 Kxa5 13. Kxb3 ) 7... Kb4 8.
Kd4 Kxb3 9. Kd3 Kxa4 10. Kc4 { Black king is trapped. Draw.}  ) 5. b4 ( 5. Kg2
$2 $19 Kf4 6. b4 axb4 7. a5 b3 8. a6 b2 9. a7 b1=Q 10. a8=Q Qc2+ 11. Kg1 Qd1+
12. Kg2 Qe2+ 13. Kg1 Qe1+ 14. Kg2 Qg3+ 15. Kf1 Qf3+ { And black takes
opposition, which is necessary to promote g-pawn.}  16. Qxf3+ Kxf3 17. Kg1 Kg3
18. Kh1 Kf2 19. Kh2 g3+ 20. Kh1 g2+ 21. Kh2 g1=Q+ ) 5... axb4 6. a5 b3 7. a6 b2
8. a7 b1=Q 9. a8=Q { This is a bit complicated, but according to tablebase,
this is draw.}   


17: <pre><code>8/8/8/5kp1/p7/P4K2/1P6/8 b - - 0 1
</code></pre>

<p>White just played Kf3, thereby gaining the opposition.</p>

<p>If there were no queenside pawns, what is on the kingside would be a "book" draw. That's because the White king can maneuver himself into a stalemate position on his first rank.</p>

<p>But in this position, if the White king can't move, White has to move the b pawn to b3, or to b4 via b3. In either event, Black's a pawn takes it, queens, and wins for Black.</p>

<p>Or does it?</p>
 3831: <p><strong>The position is definitely lost for white.</strong> </p>

<p>You can convince yourself about this by checking in an <a href="http://chessok.com/?page_id=361" rel="nofollow">endgame tablebase</a>. White either has to allow the g-pawn promotion or let his king be "stalemated", forcing him to push the b-pawn and be checkmated soon thereafter.</p>

<pre><code>[Title "Best play according to an endgame tablebase"] 
[fen "8/8/8/5kp1/p7/P4K2/1P6/8 b - - 0 1"]

1... g4+ 2. Kg3 Kg5 3. Kf2 Kf4 4. Ke1 g3 5. Ke2 Ke4 6. Kf1 Kf3 7. Ke1 g2 8. Kd2 g1=Q 9. Kc3 Qc5+ 10. Kd3 Qd5+ 11. Kc2 Ke4 12. b3 Qxb3+ 13. Kc1 Qa2 14. Kd1 Kd3 15. Ke1 Qe2# 0-1
</code></pre>

<p>Or...</p>

<pre><code>[Title "Example scenario without g-pawn promotion"]
[fen "8/8/8/5kp1/p7/P4K2/1P6/8 b - - 0 1"]

1... g4+ 2. Kg3 Kg5 3. Kg2 Kf4 4. Kf2 g3+ 5. Kg2 Kg4 6. Kg1 Kf3 7. Kf1 g2+ 8. Kg1 Kg3 9. b3 {or b4; forced, since the king cannot move} axb3 10. a4 b2 11. a5 b1=Q# 0-1
</code></pre>
 9030: <p>Black wins.</p>

<p>Black has a distant passed pawn and Blacks pawns are more advanced. White is bound to defend against g-pawn, while Black can do anything with a and b pawns. And White cannot win a pawn race, because Black is more advanced.</p>

<pre><code>[Event "Original Position"]
[Site ""]
[Date ""]
[Round ""]
[White ""]
[Black ""]
[Result "0-1"]
[FEN "8/8/8/5kp1/p7/P4K2/1P6/8 b - - 1 2"]
[Setup "1"]

2... g4+ 3. Kg3 { Option 1, defending against g-pawn, fails.}  ( 3. Ke3 { Option
2, counter attack on the other side, which fails also, because Blacks pawns are
more advanced, Black wins the race.}  3... Ke5 4. Kd3 Kf4 5. b4 axb3 6. a4 g3
7. a5 g2 8. a6 g1=Q ) 3... Kg5 4. Kg2 Kf4 5. Kf2 g3+ 6. Kg1 Kf3 7. Kf1 g2+ 8.
Kg1 Kg3 9. b4 axb3  
</code></pre>

<p>However, if Black wouldn't have a-pawn that advanced, White could catch Black and avoid promotion after dealing with g-pawn.</p>

<p>For example:</p>

<pre><code>[Event "Queenside Pawns Shifted"]
[Site ""]
[Date ""]
[Round ""]
[White ""]
[Black ""]
[Result "1/2-1/2"]
[FEN "8/8/8/p4kp1/P7/1P3K2/8/8 b - - 1 3"]
[Setup "1"]

3... g4+ 4. Kg3 Kg5 ( 4... Ke5 5. Kxg4 Kd5 6. Kf4 Kc5 7. Ke5 ( 7. b4+ axb4 8.
Ke3 b3 9. Kd2 Kb4 10. Kc1 Kc4 11. Kb2 Kb4 12. a5 Kxa5 13. Kxb3 ) 7... Kb4 8.
Kd4 Kxb3 9. Kd3 Kxa4 10. Kc4 { Black king is trapped. Draw.}  ) 5. b4 ( 5. Kg2
$2 $19 Kf4 6. b4 axb4 7. a5 b3 8. a6 b2 9. a7 b1=Q 10. a8=Q Qc2+ 11. Kg1 Qd1+
12. Kg2 Qe2+ 13. Kg1 Qe1+ 14. Kg2 Qg3+ 15. Kf1 Qf3+ { And black takes
opposition, which is necessary to promote g-pawn.}  16. Qxf3+ Kxf3 17. Kg1 Kg3
18. Kh1 Kf2 19. Kh2 g3+ 20. Kh1 g2+ 21. Kh2 g1=Q+ ) 5... axb4 6. a5 b3 7. a6 b2
8. a7 b1=Q 9. a8=Q { This is a bit complicated, but according to tablebase,
this is draw.}   
</code></pre>
