  Point processes are an essential tool when we are interested in where in time
or space events occur. The basic starting point for point processes is usually
the Poisson process. Over the years, Stein's method has been developed with a
great deal of success for Poisson point process approximation. When studying
rare events though, typically one only begins modelling after the occurrence of
such an event. As a result, a point process that is conditional upon at least
one atom, is arguably more appropriate in certain applications. In this paper,
we develop Stein's method for conditional Poisson point process approximation,
and closely examine what sort of difficulties that this conditioning entails.
By utilising a characterising immigration-death process, we calculate bounds
for the Stein factors.
