Who is at fault for car 1 when car 2 slammed his brakes on and car 3 hit car 2 and car 2 hit car 1?

Car 3 would be At Fault for all damages. From the description it sounds like car 2 had to make a stop and car 3 had either enough speed or weight to force car 2 into car 1. Car 3 should have allowed enough space in front of it to avoid any crashes. Now, if car 2 had hit car 1 and then a moment later car 3 hit car 2, car 2 would be at fault for car 1 and car 3 would be at fault for car 2. In an event like this, make sure a POLICE REPORT is made.