  Recently an alternative way to quantify Bell nonlocality has been proposed
[Phys. Rev. A {\bf 92}, 030101(R) (2015)]. In this work we further develop this
concept, the volume of violation, and analytically calculate its value for the
spin-singlet state with respect to the settings of the first Bell's inequality.
These settings correspond to three directions in space, or three arbitrary
points on the unit sphere. It is shown that the triples of directions that lead
to violations in local causality correspond to $1/3$ of all possible
configurations. From the perspective of quantum communications, this means that
two distant parties that were capable of align their measurements in one
direction only (the remaining direction in each site being random), have a
probability of about 33.3$\%$ to be able to certify their entanglement.
