This problem is an extension of Beginner Exercise 96.
Because of shortage of liberties created by the marked stone, White cannot reduce Black's liberties at a (which would be atari and auto-atari, but has to capture with first. So wins the capturing race by one move.
Directly reducing White's liberties at 1 is wrong. White 2 is the vital point, and Black 3 does not help. Note that White 6 has to atari at the correct point, playing 6 at a is a big mistake.