Correct definition of distribution for request type generation

I am trying to figure out if what I did when developing some simulations can be considered a crime or not (in math world ofc :D). Basically, I am developing a simulation, where one of the parameters is request type , let’s consider that there are 3 request types: A,B and C. Initially I assume that the requests are distributed uniformly (so I use Uniform Distribution to generate a sample of required size). At some point, I would like to breach the harmony, and make some variations in request types, so for example requests of type A start to dominate in the sample. For the purpose I am using Poisson Distribution, but since I am limited in the number of request types, I cannot accept certain values (3 for example is already out of range, since I do not have request of type D). What I am doing in this case, I am simply discarding the value and taking the next one.
So there are two questions which would help me to understand if I am doing this correctly:

1) Since I am not very strong at math, it is already the second day I am thinking about it and wondering if I can actually do this and use these simulation results in my further research work (of course I describe well the process, but still).

2) If my approach is incorrect, which distribution should be used to generate my request types (I have been looking into Geometric Distribution as well, but I would also need to discard values at some point anyways)

Thanks 🙂

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