A Dyson sphere around a black hole

Black holes don't suck anything in. They just have very strong gravity relative to their size. So just like a space probe would drop into the sun if it got too close, things can get into an inescapable orbit around a black hole. If you can build a Dyson sphere around a star you can build one around a black hole of a similar mass.

> So just like a space probe would drop into the sun if it got too close

The probability for this to happen is actually quite low, ie. it's suprisingly hard to "hit" the sun. The reason is that unless you put the probe on a completely straight path to the sun (which is hard because the sun is so small in terms of its solid angle on the sky), it will have some angular momentum and probably spin around the sun and come right back (more or less).