The distribution of prime divisors in composite almost-prime numbers

Let $n$ be a composite almost-prime number, and write $\omega(n)$ for the number of its prime divisors. Distribution conjecture. There exists an $\epsilon<1$ such that

$$\# \left\{p\mid n\ \middle|\ \omega(p-1)>2\right\}<\varepsilon\omega(n)$$

is satisfied for infinitely many composite almost-primes $n$. The preceding restrictions in the source concern prime divisors $p$ with $\omega(p-1)>2$; the conjecture predicts that such divisors form a relatively small proportion for infinitely many composite almost-primes. Its resolution is not specified in the source.