Well ultimately the PDF has to have a probability that reflects the chance of something being picked.
You start off with a state space and then introduce constraints or assumptions to form your PDF.
The first thing is to define the scope of all possible atomic events that can happen. The second is to introduce the assumptions and extra constraints that narrow the PDF down to a specific form which will be used for sampling, and the next thing will be to use a technique like MCMC based pseudo-random algorithms that allow you to draw a pseudo-random sample from said distribution.
The thing about describing the state-space is that you will want to look at the largest atomic events that you are interested in and then define them mathematically. You can use all the set theory notation to define sub-sets and also the actual state space.
Once you do this mathematically, it will be much easier to go from that and then introduce some compact assumptions (like the probability is proportional to the inverse of the weight as discussed above) and then you will generate your PDF to sample from.
I'd recommend you do the above: define the state space first using the math terminology and then define the constraints and assumptions you use. Then take this and define the event of interest that corresponds to a single sample. Then from this you will get a better chance of getting a specific mathematical expression or at the very least, advice leading to that.