How about the following:
playerList = [player1, player2, player3]
playerProb = [x, y, z] # Must add up to 100
selected_player = playerList[-1]
percentage = randint(100)
percentCount = 0
for Idx in range(len(playerList)):
if percentage < percentCount + playerProb[Idx]:
selected_player = playerList[Idx]
percentCount += playerProb[Idx]