Molar concentration of water and pKa value By defintion, $\mathrm pK_\mathrm a$ value is defined as
$$\mathrm pK_\mathrm a = -\lg ([\ce{H2O}] K_\mathrm{eq})$$

Consider the reaction:
$$\ce{HCl + H2O &lt;=&gt; H3O+ + Cl-}$$

The Eq constant of $\ce{HCl}$ is defined as

$$K_\mathrm{eq} = \frac{[\ce{H3O+}][\ce{Cl-}]}{[\ce{H2O}][\ce{HCl}]}$$

Why is molar concentration of water fixed at 55.5? Wouldn't it depend on the extent of ionization?
For most practical purposes, we assume that the aqueous solution is dilute and that the concentration of water is constant, that is, $[\ce{H2O}] \approx 55~\mathrm{M}$. This is the standard that is used to define the ionization constant of water, $K_\mathrm{w}$. 

If the equation $1\times 10^{-14}~\mathrm{M^2} = [\ce{H3O+}][\ce{OH-}]$ didn't hold (at $25~\mathrm{^\circ C}$) then we would have to come up with other equations for acid-base equilibrium. Even for strong acid/base dissociations we approximate the equilibrium equation with full dissociation (i.e. one forward arrow).

I recommend reading pp 12-15 of the following if you want a more theoretical treatment of strong acid/base dissociation where activities are used: http://www.chem1.com/acad/pdf/c1xacid2.pdf