How likely would a habitable world be that orbits a gas giant that itself is orbiting a larger gas giant? Assuming one exists, what are the likely conditions?
It's hard to say without any actual examples of moon of moons in our own solar system to use as models, but I'd expect it to be pretty rare. The first factor to consider is that your habitable world would be far more inclined to orbit the bigger gas giant meaning that smaller one would likely need to maintain a wider orbit than any moon in our solar system to keep its big brother from stealing its moon. The farthest moon from Jupiter has about a 14,600,000 miles orbital radius and even it does not have a moon of its own. If you need a 15x super jupiter as is implied in the comments, then the minimum orbit could be significantly greater than this. Small fast orbits won't help you as much as some have theorized, because the stronger pull of a larger planet will still rip the small moon away regardless of speeds if the big gas giant is too close to the smaller one.
So, the biggest problem here is that you want a habitable world. Even with an orbit as small as Callirrhoe you'd be looking at massive seasonal changes as the world gets closer to and farther from the star by a factor of ~0.3au per year. If you tried putting that gas giant system into the goldilocks zone, winter and summer would be like going from Venus's orbit to Earth's Orbit every time the small gas giant orbits the bigger one. So, even if life could evolve here, human life probably could not survive.
for the best chance for this to be possible, main sequence stars are pretty much out. Yellow suns are too small for that kind of variance to not be devastating and blue suns tend to go boom way to fast for life to have much time to evolve. A red giant might work, but it is my understanding that red giants have periodic novas that would likely kill off the planet every so often.