What causes inhalation during breathing?
Other than the branching, gas filled spaces within the lungs themselves, there are no other spaces within the trunk and above the diaphragm that contain gas - for a normal healthy lung. All the other space is filled with either tissue or fluid that serve to extend any pressure applied by the muscles you mentioned to the pleural sac that surrounds the lungs - like a hydraulic device. It's only the gas space that expands in volume and this is what causes air to move into that space through the upper airway. Exhalation is caused by elastic recoil - the springing back of this compartment.