If you presume something, it means you act as though it's true before all the evidence is in. If you are presumed to be the fastest runner, don't get too cocky — that word implies that you haven't actually raced yet.
To presume is to take something for granted. The famous quote “Dr. Livingstone, I presume?” comes from the explorer Henry Morton Stanley, who ran into the explorer David Livingstone in the wilds of Africa in 1871. It’s funny because these were the only two white men known to be in that part of Africa at the time.