Bricks, Masonry, Asphalt and Concrete - Grinding a 3 inch wide slope for drainage?

I need to find a way to improve drainage on a 3 inch wide area (11 ft long) on the back wall of my house. The previous owner enclosed a patio and raised the level of the concrete, They placed the new back wall about 3 inches from the edge of the concrete. The problem is the slab is not sloped away from the house, it is level and in one spot has a lip, as a result water seeps into my house every time it rains. I need to find a way to grade the existing strip of concrete so that it will actually drain away from the house. Some solutions I can think of:

-Grinding a slope into it (sounds time consuming and tricky)
-Cutting notches with a diamond blade (seems un-sightly)
-Building a slope with mortar (negative affects?)

what do you think?

check into a floor grinder, some rental stores carry ones that will work for that, otherwise a stone for a hand grinder but that would be a little slow.

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