Assuming everyone takes a -300 favorite, that would mean the chance of the team winning would be about 75%. If you bet 3 teams who have a 75% chance of winning in a parlay, the chance of you losing the parlay is 58% (1-0.75*0.75*0.75 = 1- 0.42 = 0.58).
That means the chance of YOU losing is 58%, but you need to keep in mind that a lot of people will be picking the same teams. Looking at this week's card, there are 4-teams that will be on almost everyone's selection of 3 teams, there are 4 different selections of 3-team parlays that you can have. If one of the 4 teams loses, only one of the 3-team parlays will survive and 3 will lose. So the percentage of people who will lose is:
So 58%* 3/4 = 43.5%
(Fish, did you do "58% divided by 4" to get 14%? If one team loses, 3 different parlay combinations are ruined, so it should be 3/4 and not 1/4, no?)