  We revisit the Kahn-Kalai conjecture, recently proved in striking fashion by
Park and Pham, and present a slightly reformulated simple proof which has a few
advantages: (1) it works for non-uniform product measures, (2) it gives
near-optimal bounds even for sampling probabilities close to 1, (3) it gives a
clean bound of $p_c \leq 4q_c \log_2 (7\ell)$ for every $\ell$-bounded set
system, $\ell\geq 1$.
