  Employing the volume of quantum steering ellipsoids (QSEs) as a measure on
the fifteen-dimensional convex set of two-qubit states, we estimate the ratio
of the integral of the measure over the separable states to its integral over
all (separable and entangled) states to be 0.0288. This can be contrasted with
the considerably larger separability ratios (probabilities) of $\frac{8}{33} =
\frac{2^3}{3 \cdot 11} \approx 0.242424$ and $\frac{25}{341}=\frac{5^2}{11
\cdot 31} \approx 0.0733138$ that various forms of evidence point to with the
use of the prominent Hilbert-Schmidt and Bures measures, respectively. The
questions of whether the ratio in the QSE setting can be more precisely
obtained or even exactly computed, as well as whether a metric can be
constructed, the volume element of which yields the measure, remain to be
addressed. We also investigate related issues pertaining to absolute
separability. Further, we examine the behavior of the separability
probability--constant in the Hilbert-Schmidt case and decreasing in the
Bures--as a function of the Bloch vector norm in the QSE instance. It appears
to increase approaching the pure state boundary.
