Duchene, 19, was selected third overall in 2009. He led all rookies in scoring with 55 points (24 goals, 31 assists) in 81 games, shared the rookie goal-scoring lead with the New York Islanders' John Tavares and ranked second among rookies in assists.
Howard, 26, was picked in the fourth round in 2003. He was 37-15-10, with a 2.26 goals-against average and .924 save percentage.
Myers, 20, was taken 12th in 2008. He led the Sabres in ice time at 23:44 and was fifth on the team with 11 goals and 37 assists. He was one of four rookies to play all 82 games.
The winner will be announced June 23 during the NHL awards show in Las Vegas.