Is capturing on empty square with a pawn legal? How is it possible to move c4 to b3?
This type of capturing with pawn called capturing en passant.

Here's the rule explained on Wikipedia:


  When a pawn advances two squares from its starting position and there
  is an opponent's pawn on an adjacent file next to its destination
  square, then the opponent's pawn can capture it en passant (in
  passing), and move to the square the pawn passed over. This can only
  be done on the very next move, otherwise the right to do so is
  forfeit.