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Yeh, the illusion of car floating is easy to get when using lightsources that casts too soft shadows (HDRI, big area lights and whatnot) - btw.. is that why your shadows so dark.. to "hide" the float effect? :P Cuz i just think they are too dark.. again :P
You should look into Ambient Occlusion - You can use it for the entire render, or as a "contact patch" only. If latter, then apply it only on the ground and tweak the settings so the AO has the desired effect.
You could also use regular lights, and these can give better results. But this method required a lot more work and tuning.