The move to convertible devices is being driven by and catering to enterprise users. Microsoft is in the lead here with the Surface, and they're trying to extend this to their phones but they may not be able to overcome the handicap of nobody wants their phones. Apple is playing from behind here because there's walls between iOS and OS X that they won't cross, but they have inroads into the enterprise space, they have enough native iOS productivity apps that work well on tablets (Adobe and ironically Microsoft are both heavily into the iOS productivy app space, and that's a huge part of the market) that the iPad Pro is... unappealing to me personally but quite possibly will be successful in the marketplace.
Google has... Chromebooks, which have no apps and no market penetration outside of the very, very captive education market (where IT administrators just want computers so locked down that teenagers can't do too much damage). And they have Android, which (in tablets at least) has almost no enterprise penetration and very little in terms of productivity apps. And the merging of ChromeOS with Android in order to tackle the enterprise market and the Surface line and the iPad Pro makes a lot of sense. But I'm not sure either papers over the other's flaws enough to make it viable, and I'm definitely not convinced that they're going to be able to be combined in a way that incorporates what ChromeOS does well that Android doesn't, like system software updates.