To determine the correct order of basicity for the given compounds, we need to consider the availability of the lone pair of electrons on the nitrogen atoms for protonation.

1. The basicity of a compound is influenced by the electron density on the nitrogen atom. The more available the lone pair of electrons on the nitrogen atom, the stronger the base.
2. Compound III: This compound is pyrimidine, which has two nitrogen atoms in a six-membered ring. The lone pair on the nitrogen atom is not involved in resonance with the ring and is therefore more available for protonation, making III more basic.
3. Compound II: This is pyridazine. Here, the involvement of the nitrogen's lone pair in resonance is relatively less compared to pyridine, thus, II is moderately basic.
4. Compound I: This is pyridine. The lone pair of electrons on nitrogen is involved in resonance with the aromatic ring, making it less available for protonation. This makes pyridine the least basic among the three.

The correct order of basicity based on the availability of the lone pair electrons is: III > II > I.

Conclusion: The option III > II > I is thus the correct answer.