Korean Mahjong is an excellent way to play the game if you only have three players. By no means is it any less challenging than say, four player Hong Kong mahjong. If anything, it will show you a very different world of mahjong. There are various ways to play the game with only three players, the following are options that you can chose from.
Invisible Fourth Player
The game can be played as though there is a fourth player. In this case you can decide to not include the last 13 tiles of the wall or not in the game (as though there was a fourth player keeping that many pieces not in the wall). This is optional, both have its advantages and disadvantages. In any case, playing with the invisible fourth player means there is one player who is not one of the winds at any given time. A full round will still be 16/32 games. There are no other changes to the rules and you play as though you would four player mahjong.
This version creates a few very unique features in the world of mahjong. First, one wind is entirely omitted (usually the north wind). It is replaced by a unique suit of its own (only two tiles of the north wind). You may also decide to add the 1 and 9 bamboo tiles to the game, which are considered honour tiles (though a pong of these do not give any additional points). The special suit (the two pieces of the north wind) can only be made as a pair. Having this pair is worth a point and can be included towards your minimum points. You may chose to build four walls or a triangular wall with sides of 17 long. There is no ghost player nor ghost tiles (all the tiles are used). As there are only three winds a full round lasts only 9/18 hands. The game goes very fast.