To dream that you took the third place in some kind of competition, means that you are doing great and the results of your hard work already showing up. If you felt very unhappy, because you won the third place and not the second or first one, then such dream means that you are the person who like to be leader and first in whatever you do. The one who is happy because of accomplishing third place is the person that is happy for any achievement he does. Keep going that way, because you will succeed in your life later on because of your positive attitude towards the life.
Read more about dreaming of Third place in other dream meanings interpretations.