Canonical ensemble - Proportionality of probabilities - Huang Section 7.1 [duplicate]

From the book I am currently reading.

Consider an isolated composite system made up of two subsystems whose Hamiltonians are, respectively, $\mathcal{H}_1(p_1,q_1)$ and $\mathcal{H}_2(p_2,q_2)$, with number of particles $N_1$ and $N_2$ respectively. We assume that $N_2 >> N_1$ but that both $N_1$ and $N_2$ are microscopically large. We are interested in system 1 only. Consider a microcanonical ensamble of the composite system with total energy between $E$ and $E + 2 \Delta$. The energies $E_1$ and $E_2$ of the subsystems accordingly can have any value satisfying $E < E_1 + E_2 < E + 2 \Delta.$ Although this includes a range of values of $E_1, E_2$, the analysis of Section 6.2 shows that only one set of valus, namely $\bar{E}_1, \bar{E}_2$ is important. We assume that $\bar{E}_2 >> \bar{E}_1$. Let $\Gamma_2(E_2)$ be the volume occupied by system 2 in its own $\Gamma$ space. The probability of finding system 1 in a state within $dp_1 dq_1$ of $(p_1,q_1)$, regardless of the state of system 2, is proportional to $dp_1 dq_1 > \Gamma_2(E_2)$, where $E_2 = E - E_1$.

I think the author assumes that many things are intuitive which to me they're not. Where does this proportionality come from?