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?

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Thank you