To perform importance sampling on a light source, a probability density function must be provided for the sampling distribution. For most light sources, a valid probability distribution can be found, but point lights and pure directional lights (directional lights which emit light exclusively in one direction, with 0 spread angle) do not have this property, as there is only one valid light path connecting them with any given point. This would require an infinite probability density, which would result in an infinitely small light contribution due to importance sampling. My question is: how can these light types be sampled without introducing bias?
I've asked more specifically about the mathematics behind this on the Mathematics Stack Exchange, but seeing as I received no replies there, I think this would be a more appropriate place to ask.