Categorical Variational Inference

How to modify the Categorical distribution to obtain a support over -1,0,1 and not the default 0,1,2 for a three event experiment. Basically I want to apply variational inference by choosing the categorical distribution as my variational posterior. and would want to update its parameters (distribution probabilities)
and sampling this distribution should give me -1,0 and 1 and not 0,1,2