Generate multiple random samples from given probability distributions with their sum equal to a given num

I have three random variables x,y,z with different probability distributions. I want to generate numbers drawn from these three random variables with a constraint that these three number sum to a given number. How could I achieve this in python? I've found a similar problem and solution here when the random variables have uniform distribution, but it doesn't seem to generalize to non-uniform distribution scenarios? Generate multiple random numbers to equal a value in python .