What is the correct order of priority when multiple players want to claim the same discard?

When multiple players want to claim the same discard, winning claims (mahjong) always take priority over everything else. After that, a pung or kong claim takes priority over a chow claim. If two players both want to pung the same tile, the player whose turn comes next in the playing order takes priority. Chows can only be claimed by the player whose turn is immediately next; no other player may claim a discard for a chow.