If the order of these winners in pairs is important, then the number of ways is 3*2 = 6

        AB, AC, BC, BA, CA, CB.



If the order of these winners in pairs is not important, then the number of ways is 3

        AB, AC, BC.



Since the wording in your post does not allow to distinct between these two 
possible configurations, it is not possible to give a unique answer.



The correct way to ask the question is THIS:


    Racers A, B and C have the greatest chance of winning the race. 
    How many different ways can the first two positions be placed

    (a) if the order in pairs is important ?

    (b) if the order in pairs is not important ?



Then the questions are clear, and the answers are clear, as well.