0.0001%
Yeah, they're 11.5 games up in the East and the only even remotely good teams they have on the final two months of the schedule are the Giants and Dodgers. Arguably the Yankees. Otherwise, they get to feast on the rest of the NL East and shitty teams like the Cardinals, Rockies, Pirates and Cubs.
For the Braves to lose the division would require a 1969 Cubs-level meltdown in August and September.