The fraction alpha of O2(b 1SIGMA(g)+, upsilon=0) molecules formed when O2(A 3SIGMA(u)+, upsilon=8) is quenched by molecular oxygen was obtained by comparison of the intensities of the excitation spectra of O2(A 3SIGMA(u)+, upsilon=8) and O2(b 1SIGMA(g)+, upsilon=2), both observed via the O2(b --> X, (0,0)) emission at lambda=762 nm. The result is alpha=0.25 +/- 0.09. An approximate value for the fraction of O2(b 1SIGMA(g)+) formed by quenching by N2, beta, is 0.75. The consequences for the contribution to the excitation Of O2(b 1SIGMA(g)+, upsilon=0) in the nightglow of the lower thermosphere of the Earth are discussed.