What is the general form of an arbitrary element of $\Omega_p$ ? Here "general form" means something like $\frac{a}{b}$ for an element of $\mathbb{Q}$ or $\sum_{i>-n_0} a_i p^i$ for an element of $\mathbb{Q}_p$.
$\Omega_p$ is the spherical completion of $\mathbb{Q}_p^{alg}$, the algebraic completion of $\mathbb{Q}_p$. Be aware that this is different from the better known $\mathbb{C}_p$ (for instance, $(\mathbb{P}^1(\mathbb{C}_p))^{an}$ has type IV points, and $(\mathbb{P}^1(\mathbb{\Omega}_p))^{an}$ has none).