If Light Has No Mass, then why is It Affected by Black Holes
According to General Relativity. A photon always travels by the shortest distance between the two points, and around a black hole, the distortion of space-time is extreme. So light(Photon) is appear to be bend around the black hole. As a space-time wrap around a massive object light seems to be bend around it.
In a more simple way photon is not fall off inside the black hole, but it just cover its own shortest distance trajectory.
The illustration diagram is given below for more understanding,