How will citric acid be deprotonated by pyridine?
The table on the right looks like a standard group of acids shown to illustrate the effect of inductive withdrawing on carboxylic acid pKa. The first two structures are relevant to the question. The table may have been copied from somewhere else because it had both structures on it. Two of the pKa values in the table are every similar to two of the pKa values given in the question. The fluoroacetic acid is a fine distraction; you are correct in thinking that it is not involved.


  As for figuring out which of citric acid's three carboxylic acids is deprotonated first...


Citric acid has three carboxylic acid groups of two different types. Can you see that? One of the acids is closer to the OH group than the other two. Which acid or acids look more like the first entry in the table (except jammed onto the citric acid structure)? Which acid or acids look more like the second entry on the table? Once you have made that distinction, you should be able to use the pKa data on the table to determine which of the three carboxylic acid groups in citric acid is the most acidic (goes with the 3.13 pKa).