# Probability Theory: Likelihood Function definition question

I have question on whether the Wiki definition is correct. Defined on Wiki as:

a)
$$mathcal{L}(theta mid x) = p_theta (x) = P_theta (X=x)$$
where $$p_X$$ is the probability mass function defined as:
$$p_X(z) = P(X = z) = P({s in Omega : X(s) = z})$$

Then used as follows in an coin toss example on Wiki:

b)
$$P(HH | P_H = frac 1 2) = (frac 1 2)^2$$
$$mathcal{L}(P_H = frac 1 2 | HH) = frac 1 4$$

Is the Wiki (a) definition correct? I ask because $$P_theta(X = x)$$ appears adding an extra parameter vs the PMF $$p_theta(x)$$. If it is correct, can someone explain why the RHS of (a)?