This is the usual behavior. When the engine is running, it is generating a vacuum, which pulls on a diaphragm in the brake booster. This is what is called "power brakes". It uses engine vacuum to help push hydraulic fluid thus reducing the amount of pressure you must apply to the brake pedal. When the engine is off your foot has to make up for the force that engine vacuum usually applies, which makes the pedal feel much more firm.
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