Drill hole flush to the floor?

We are having a flooding problem. I want to drill a small hole where the step riser meets the floor. It needs to be flush with the floor to let water out so it can be diverted to a drain. The step and floor are concrete. I cannot find any tool that will drill flush so the water can get out. The hardware stores don't have anything that will do this. Any ideas what I can do? I think there is an aquifer under the step that eventually fills up in heavy rain. It is a very old house and it seems that new building around it has diverted the water runoff during heaviy rain. It has turned into a nightmare everytime there is a storm.