How can I model the data having three continuous variables to find their joint probability?

I have the data consisting of three continuous variables say A,B,C which forms a bayesian network (A -> C, B -> C) where A and B are independent. I need to find the joint probability of the entire network which is mathematically given by
P(A,B,C) = P(A) * P(B) * P(C / A,B)
Theoretically , it is fine. But, how can I find the probabilities and conditional probabilities given the variables are continuous. I’ve googled a lot about these. A continuous variable is represented using a PDF, but how can we find probabilities from a PDF. Any help would be appreciated.

When you write down your model P(A,B,C) = P(A) * P(B) * P(C / A,B), you already have your probabilities, represented as a continuous function that takes 3 input and output 1 value. What you are asking is actually how you can use this PDF. So, ask yourself, when you said you want a probability - a probability of what? Some example question could be: what is the probability of A=a, B=b and C=c? Easy, compute P(A=a, B=b, C=c). More difficult question: what is the probability of P(C | A=a)? Here you want to marginalized out B, and get a function that takes 1 input and 1 output.