posterior distribution conditioned on a second parameter

[JJstar]

If you have 2 parameters a and b and a observed data set x, and wish to calculate the posterior distribution of a given b is the following true

P(a|b,x) proportional to P(a,b| x)

Where proportionality is in a.

I had wrote this down somewhere but can't remember why or if it is right.

Thanks in advance for any help