Since we don't know the exact value of a scholarship, lets assume it is zero (it isn't, but it doesn't matter for the math on this).
If prestige had been equal, the odds should have looked like this
Team A 38% (240 APs/625 APs from all three teams)
Team B 33% (205 APs/625 APs)
Team C 29% (180 APs/625 APs)
In order to figure out how Team A got to 51%, some simple algebra
.51 = (x+240)/(x+625)
x=160 (rounded down)
When you give Team A an additional 160 points for a prestige bump, the numbers come out as
Team A 51% (400 APs+prestige/785 total effort expended)
Team B 26% (205 APs/785)
Team C 23% (180 APs/785)
With some rounding here and there, that roughly correlates to what the exact posted odds were. Team A's had a prestige advantage of 1/3rd of a letter grade (B+ vs. B) and that advantage almost equaled all of the effort put in by Team C.