Shadow floor without shadow for ambient light?

Hi,

is it possible to create a shadow floor that shows shadows for directional lights but not for the ambient light?

I want to get rid of the shadow marked red in the picture but want to keep the one marked green.

Also I want to be able to have transparency when rendering PNG files.

If I set transparency on the floor to 0, the ambient shadow does not appear but also I don't get transparency in PNG anymore.

The problem gets even worse when having a black background (please see second picture).

Any ideas?

Alex

SolidworksPhotoworks