Note that that's in the sense of angular separation, as viewed from the ground. They're physically hundreds of kilometers apart.
edit: (Geostationary orbits are ~42,000 km from the Earth center-of-mass; each degree of angle is an arc of ~700 km).
But some debris (in particular slower pieces) will probably oscillate around the geostationary orbit giving it countless chances of hitting other satellites.
Has someone modelled this for example in Kerbal space program?
Almost all of the debris will have orbits which intersect their orbit of origin.