Considering Google have invested a fair bit of cash into Uber which might be a tax write-off for Google, I would probably say we are going to see Google try and buy Uber out instead. Cutting off their maps access would probably open up a can of worms for Google as Uber would undoubtedly take legal action (and they have the funds to really go for it), there could be a little bit of conflict of interest happening here as Google have access to inner workings of Uber's business model and the business itself.

But having said that, there is probably nothing stopping Google from creating a driverless car Uber rival, it would fall outside of the realm of being a true direct competitor as there are no drivers. But are driverless cars at a point where they can be rolled out on a larger scale? Seems there is a lot of regulation and process to abide by before that starts to happen, maybe a controlled rollout?

I am surprised Google haven't tried launching their own airline yet, it would probably be undeniably easier than a ridesharing network of driverless cars.