Indistinguishable encryptions in the presence of an eavesdropper equivalence
I've found an answer to my question, I'm going to post it because it can be useful to someone out there.

The point is that, if we assume that $\mbox{Prob}[\mbox{Priv}_{\mathcal{A},\Pi}^{\mbox{eav}}(n)=1]\leq 1/2+negl(n)$, then $\mbox{Prob}[\mbox{Priv}_{\mathcal{A},\Pi}^{\mbox{eav}}(n)=0]\leq 1/2+negl(n)$ too (if this were not to happen, then we could create an adversary that solves the experiment with a better probability than $1/2+negl(n)$). 

This allows us to use the same argument I've used for proving the first inequality for getting the inequality with absolute value.