  We introduce the quark virtuality distribution [$\lambda^{2}_{q}(x)$] as an
extenson of the quark virtuality by using nonlocal rather than local quark
vacuum condensates. Our results show that the quark virtuality distribution
decreases gradually from a finite value to zero as $x$ increases. This clearly
indicates that quarks are confined inside hadrons, whereas, as $x$ approaches
zero quarks have a finite virtuality, which shows asymptotic freedom of quarks
in QCD. The present predictions are important not only for studying the
properties of QCD vacuum states, and non-perturbative QCD problems, but also
for study of the cosmological constant problem, which we have shown should be
treated using nonlocal quark vacuum condensate in the Ghost theory of QCD.
