I'm not sure what you mean by "the car behind didn't show turn signal".

If you're referring to the pink hatchback that ultimately rear-ended the SUV - the pink hatchback seems to be making a lane change to the right after passing. The driver seems to have signaled and looked to the right to clear his/her blindspot at the same moment the SUV ahead slams on the brakes. It really seems like bad luck, that traffic would suddenly stop at the exact moment the driver of the pink hatchback looks to the right to change lanes.