Gravity doesn't slow down light, it distorts space/time makeing it 'appear' to be travelling at a different speed. The speed of light is constant. Big difference.
The event horrizon is the point where the space warping from the gravity well is so strong that it turns back in on itself. The 'fact' that 'nothing escapes from a black hole' might not be completly true though. The links bellow will keep you reading for the next few weeks.
Try these links