One way to do this would be to break this up into multiple models instead.
At the highest level, you predict the total number of shots daily. Then you use a binomial distribution to predict the probability (i.e., rate) that each of those shots is low, medium, high danger. When you go to make predictions for the rate of each shot type just normalize the rates so that they sum to 1.
If your data is shot by shot, your binomial distribution could be a bernoulli instead.