I find myself not really caring that much about the self-driving car race. Not because the technology isn't cool, it is, but because I'll likely never be able to enjoy it here in Malaysia. The three companies in the race don't have a big presence here. Uber lost to local competitor Grab and left the country, Google doesn't even sell it's Pixel phones here, and Tesla doesn't exist in Malaysia.
Having said that though, to answer your question, I'd probably go for Uber to win too. They already have the ride sharing infrastructure on a mostly global scale. Even if Tesla or Google were to win the race to get road-ready self-driving cars, they'd then need to win the ride-sharing market too. Uber is already half way there and just needs to figure out the self-driving bit.