1. 1903 Boston Americans (Red Sox), down 1-3, won World Series 5-3 over Pittsburgh (best of nine format).
2. 1925 Pittsburgh Pirates, down 1-3, won World Series 4-3 over Washington.
3. 1958 New York Yankees, down 1-3, won World Series 4-3 over Milwaukee.
4. 1968 Detroit Tigers, down 1-3, won World Series 4-3 over St. Louis.
5. 1979 Pittsburgh Pirates, down 1-3, won World Series 4-3 over Baltimore.
6. 1985 Kansas City Royals, down 1-3, won World Series 4-3 over St. Louis.
44 teams have been up 3-1 in WS play. 38 went on to win the series, the six above were the only exceptions. Thus 86.3% of the teams up 3-1 won the series.
I bet it happens way more than that here in ATG.