We could derive probabilities from betting odds; instead we derived them from ratings, specifically from Elo ratings before the tournament . Ratings give one estimate of probabilities, as described here.
With 16 matches there are 2^{16} possible combinations of wins and losses. We simply calculate the likelihood of each possible combination, as well as the likelihood of the actual outcome combination (which is about 1 in 125,000). Finally we calculate the probability of seeing some combination that is more likely than 1 in 125,000 ("fewer upsets") and the probability turns out as 90%.