Note that this solution only works because the marked black stones have no outside liberties ( puts them into atari and black has no time to play at ).
If black plays 'a' this is revert to the original problems, and it's wrong. The best black can do is here. More information at long L group; it's alive in seki.
here is correct. 'a' would make black alive too, but only in seki; when black plays the group lives with points.
In a situation like this the best black can do is get a ko with here. More information at long L group. If you have been looking at this page carefully, it's obvious 'a' doesn't work for black.