Positivity at one-half for the relative covariance

Let $G(n,p)$ be the random graph with independent edge probability $p$, with each present edge oriented independently and uniformly. Fix distinct vertices $s,a,b$, and define

$$R_n(p)=\frac{\mathbb{P}(a\not\to s,\ s\not\to b)-\mathbb{P}(a\not\to s)\mathbb{P}(s\not\to b)}{\mathbb{P}(a\not\to s,\ s\not\to b)}.$$

Half-probability positivity conjecture. For $p=\frac12$ and $n\ge 6$, the relative covariance $R_n(p)$ is positive.