It is well accepted that unabsorbed as well as absorbed active galactic nuclei (AGNs) are needed to explain the nature and shape of the Cosmic X-ray background (CXB), even if the fraction of highly absorbed objects (dubbed Compton-thick sources) still substantially escapes detection. We derive and analyze the absorption distribution using a complete sample of AGNs detected by Swift-BAT in the first three years of the survey. The fraction of Compton-thick AGNs represents only 4.6% of the total AGN population detected by Swift-BAT. However, we show that once corrected for the bias against the detection of very absorbed sources the real intrinsic fraction of Compton-thick AGNs is 20+9 --6%. We proved for the first time (also in the Burst Alert Telescope (BAT) band) that the anti-correlation of the fraction of absorbed AGNs and luminosity is tightly connected to the different behavior of the X-ray luminosity functions (XLFs) of absorbed and unabsorbed AGNs. This points toward a difference between the two subsamples of objects with absorbed AGNs being, on average, intrinsically less luminous than unobscured ones. Moreover, the XLFs show that the fraction of obscured AGNs might also decrease at very low luminosity. This can be successfully interpreted in the framework of a disk cloud outflow scenario as the disappearance of the obscuring region below a critical luminosity. Our results are discussed in the framework of population synthesis models and the origin of the CXB.