What is the model year of the vehicle?
I don't know the vehicle but reading online it seems that it may have either a vacuum brake booster or a hydraulic brake booster given what booster part types are available.
If the brake pedal sinks to the floor when the engine is running then there may be a problem with the brake booster. Here’s a video that may be of some help for a vacuum brake booster. At 3:30 minutes into the video it describes why the pedal may go to the floor - faulty poppet valve in the booster.
Here’s a link that details how to test if a vacuum brake booster is working properly.
I don't know about a hydraulic brake booster but here’s the 2007-2009 GMC Yukon Service Repair Manual + Owner’s Manual. I realize that this is out of the model year range that you selected but in the Brakes > Hydraulic Brakes section, it describes the operation and repair of the hydraulic brake booster. Hopefully it may be the same for your year model.