Premiere Pro CC - Creating an interview video with multiple camera angles
Premiere Pro has a multicam-functionality which you can use. To create a new multicam-sequence, select the three clips of your three cameras in the project panel, right-click → Create Multi-Camera Source Sequence (you might also be able to do that within your existing timeline). Then, select which synchronizing method you want to use (audio works just fine most of the time).

Once you click OK, it will create a new sequence that you can insert into your timeline just like any other clip or sequence. Once you've done that, click on the screwdriver icon in the programm panel and switch from Composite Video to Multi-Camera. Then, press 0 to Toggle Multi-Cam recording (there's also a button for that hidden behind the button editor). 

Once you've done all that, you can simply playback the sequence and switch between cameras while watching (either by clicking on the different views in the program panel or using the number-keys on your keyboard as shortcuts). Premiere Pro will record the the switches and insert cuts accordingly. You can also go back and change the cuts as many times as you want.

Note that this is only one possible workflow. For some other options and more a more detailed explanation, check out the corresponding manual page.