First of all, it should be tested whether the track of the PHO even passes through the ring of geosynchronous satellites (the geostationary orbit). If it approaches to a closer distance than the geosynchronous orbit, but without also crossing the geostationary orbit (possible in 3D), the chance of a collision is simply zero. The chance of a collision would be largest in the case of the PHO approaching within the ~~ecliptic~~ **equatorial** plane, where the PHO has two chances of striking a satellite (on the way in to closest approach, and on the way out again). For any other geometry, there is only a single possible collision point. The estimate below is based on that latter scenario. Of course, given that the position of all the satellites is precisely known, in any specific case it can be determined with very high certainty whether a collision will occur or not. The estimate is thus more general in the sense that it gives us the overall probability that such a collision might happen at some point in the future, for all encounters with PHOs which certainly cross the geostationary orbit (in 3D).

Given about 600 geosynchronous satellites, an assumed spherical radius R of 4 m per satellite, the volume of geosynchronous space filled by satellites is 600 * (4/3*Pi*R^3) / (Pi * R^2 * 2 * Pi * R_G), with R_G the radius of the geosynchronous orbit (35 786 km). This gives 1.4 * 10e-5. So this is the chance that a given volume of geosynchronous space (e.g., the point where the orbit of the PHO crosses the geostationary orbit) will be filled with a satellite at a given time (e.g., the moment the PHO crosses the geostationary orbit). If we assume the PHO is point-like, this is the chance we are looking for (odds of 1 in 70 000). In fact, chances of a collision are a bit higher since the size of the PHO is non-zero, but that effect is small. But remember also that this is only the chance for PHOs which definetly cross the actual geostationary orbit, not all of those which approach to a closer distance (which is a much, much larger number).

Edit: replace "ecliptic" by "equatorial"