Teams Down 3-0 in the NBA Playoffs

In NBA history, teams with a 3-0 lead in a playoff series have gone on to win the series 100 percent of the time (110-0)
— GSWStats (@gswstats) April 24, 2015

There are 5 teams this year with a 3-0 lead in the first round of the NBA Playoffs, and as illustrated above, it's extremely unlikely any of them will blow their respective leads. But just how unlikely is it that a team down 0-3 has never come back to win the series? 

Usually the better team/higher seed will be up 3-0, but not always: this year the Wizards (East 5-seed) are up 3-0 on the Raptors (East 4-seed). Thus, I used the Log5's from this year's five 3-0 series to approximate the average chance the trailing team has at coming back and winning 4-3:

3	0	Game 4	Game 5	Game 6	Game 7	Prob Win Series
GS	NO	29.87%	15.19%	29.87%	15.19%	0.21%
WSH	TOR	48.27%	67.60%	48.27%	67.60%	10.65%
CLE	BOS	38.26%	21.23%	38.26%	21.23%	0.66%
CHI	MIL	47.77%	28.92%	47.77%	28.92%	1.91%
HOU	DAL	59.40%	39.66%	59.40%	39.66%	5.55%
						3.79%

The Raptors have the best chance to be the first team to do it, about 1 in 10. Overall, 3.79% is low, but not entirely impossible (it's equivalent to about 1 in 26). But more unlikely than a team coming back from 3-0 is the fact that no team has done it in 110 tries. Using this year's 3.79% as a proxy, (1-3.79%)^110 = 1.42%. Just like a 16-seed beating a 1-seed in the NCAA tournament, a team coming back from 0-3 is bound to happen eventually. Just ask the 2004 Red Sox.