How can pKas differ across similar protons of the same atom?
Here is a picture of citric acid.



As you noted, there are 3 carboxylic acid groups in citric acid, so there are 3 acidic protons. A chemist looking at this unionized molecule would say that the carboxylic acid group drawn on the right side of the molecule is equivalent to (the same as) the carboxylic acid group drawn on the left.  Therefore, these 2 equivalent carboxylic acid groups should have the same pKa.  The carboxylic acid group drawn in the middle of the diagram is different from the other two (it is not the same as the other two) and should therefore have a different $\ce{pKa}$.  In chemistry, groups are either the same or different.  If they are the same they must be indistinguishable in all aspects, including physical properties like $\ce{pKa}$

That said, we might expect when we treat citric acid with more and more base to see only 2 different $\ce{pKa}$'s, but that is not the case.  In actuality when we treat citric acid with base one of the two different (right and left or middle) carboxylic acid groups will ionize.  Once that happens the ionized citric acid molecule contains a negative charge.  It will be harder to ionize the molecule again and remove the second proton and place a second negative charge on the molecule (bringing like charges together is destabilizing and costs energy).  The same argument tells us that removing the third and final proton will be even more difficult because we wind up with 3 negative charges on the molecule.  As a consequence of this increasing difficulty to remove protons, we observe 3 different $\ce{pKa}$'s.