  Using an eikonal analysis, we simultaneously fit a QCD-inspired
parameterization of all accelerator data on forward proton-proton and
antiproton-proton scattering amplitudes, together with cosmic ray data (using
Glauber theory), to predict proton-air and proton-proton cross sections at
energies near \sqrt s \approx 30 TeV. The p-air cosmic ray measurements greatly
reduce the errors in the high energy proton-proton and proton-air cross section
predictions--in turn, greatly reducing the errors in the fit parameters. From
this analysis, we can then compute the survival probability of rapidity gaps in
high energy pbar p and pp collisions, with high accuracy in a quasi model-free
environment. Using an additive quark model and vector meson dominance, we note
that that the survival probabilities are identical, at the same energy, for
gamma p and gamma gamma collisions, as well as for nucleon-nucleon collisions.
Significantly, our analysis finds large values for gap survival probabilities,
\approx 30% at \sqrt s = 200 GeV, \approx 21% at \sqrt s = 1.8 TeV and \approx
%%13% at \sqrt s = 14 TeV.
