It will continue existing, at least for 4 years will have the same titles as PS4 with some companies that will do dual release, for example EA.
Eventually the price will drop, at least 50 bucks when the PS4 enters the market. Also, take into account that in the first year a lot of people will buy PS4, but not the huge market as the PS3 has some utility life and you have to wait a little because maybe the first PS4s come with some glitched things, or some crap not working totally as well as expected, so most people will wait a few months maybe a year or so, just the fanboys will purchase it in Day 1.
Game prices will remain the same I believe, or if the PS4 are at the same price they may drop 10-15 bucks, but that's all.