On the activity of liquids and solvents in equilibium constants
I concluded on this question after discussion with the physical chemistry professor at my home university, and reading some physical chemistry books.
Although many references include the concentration of water in the expression of Ka, this is incorrect: the activity of pure water is 1. In dilute solutions, $a(\ce{H2O}) \approx 1$.
Therefore, the second option is correct:
$$K_a=K_c=\frac{[\ce{A-}][\ce{H3O+}]}{[\ce{HA}]}$$
This has a direct consequence on the values of pKa for the two couples of water: $pKa(\ce{H3O+}/\ce{H2O})=0$ and $pKa(\ce{H2O}/\ce{OH-})=14$, instead of the values $-1.7$ and $15.7$ that are often found in textbooks (which result from including $[\ce{H2O}]=55.55$ mol/l).
A good article on this matter can be found here: What is the pKa of water?.
References:

B. Leyh, Department of Chemistry, University of Liège, Belgium.
Atkins, P., &amp; De Paula, J. (2006). Atkins’ physical chemistry (8th ed.). London, England: Oxford University Press.
Reid, P., &amp; Engel, T. (2006). Physical Chemistry. Philadelphia, PA: Pearson Education.