I'd like to note: While this is the current and recent future situation, that is not to say that Sony will stay out of the handheld business forever more. One of the principal weaknesses to Sony's handheld strategies from PSP to the Vita was the use of expensive, proprietary memory cards. If they designed a successor for Vita to be more accessible (internal storage and standard expandable storage, for example) and bundle it with a stream box connected to the TV, they could have a legitimate competitor to Switch.
Looking forward to getting my hands on Switch at launch!
And what games would Sony have?
Hard for me to say; it'd all boil down to their strategy. Like with PSP/Vita/DS/3DS, they could have exclusive games for their handheld or ports of older games. That's the fickle thing about the games industry. Getting developers on board to develop games is one obstacle to overcome, but if it's not enough to convince consumers, then they (developers) abandon ship pretty fast.