Determing the probability distribution of coefficients given a particular value

Say I have a set of coefficients b ={b1,b2,…bn} with their own distributions and I decided to set the value of b1 to a particular value x. How could I determine, if this question even makes sense, what the probability distributions for b are conditional on b1 being equal to x?

Is there someone who has already explored this question in a notebook that is readily available?

My end goal is a visual where the viewer can take the model, set various beta values and see how the distributions my be effected—if they are at all.

This discussion might be relevant?

Thank you