Suppose I have the conditional probabilities of $B$ given $A$ (both categorical): $$\Pr(B|A).$$ The probabilities are given as a contingency table.
Using these conditional probabilities, I can fudge a $B$ column into a dataset that has only an $A$ column. For each row in the dataset, I choose a value for $B$ at random based on $P(B|A)$ for the value of $A$ of the current row.
From my understanding, this can be seen as a model, although a quite simple one. Adding the $B$ column could be thought of as "simulating" the model.
My question: Is the term "model" applicable in this case? If so, how would such a model be called?
Somebody mentioned the term "Poisson distribution" in this context, but I was unable to align these two concepts with my limited knowledge of statistics.
See also this question on how to implement this in R.