  Knowledge about the distribution of CO emission in the Milky Way is essential
to understand the impact of Galactic environment on the formation and evolution
of structures in the interstellar medium. However, currently our insight about
the fraction of CO in spiral arm and interarm regions is still limited by large
uncertainties in assumed rotation curve models or distance determination
techniques. In this work we use a Bayesian approach to obtain the current best
assessment of the distribution of 13CO from the Galactic Ring Survey. We
performed two different distance estimates that either included or excluded a
model for Galactic features. We also include a prior for the solution of the
kinematic distance ambiguity that was determined from a compilation of
literature distances and an assumed size-linewidth relationship. We find that
the fraction of 13CO emission associated with spiral arm features varies from
76% to 84% between the two distance runs. The vertical distribution of the gas
is concentrated around the Galactic midplane showing FWHM values of ~75 pc. We
do not find any significant difference between gas emission properties
associated with spiral arm and interarm features. In particular the
distribution of velocity dispersion values of gas emission in spurs and spiral
arms is very similar. We detect a trend of higher velocity dispersion values
with increasing heliocentric distance, which we attribute to beam averaging
effects caused by differences in spatial resolution. We argue that the true
distribution of the gas emission is likely more similar to a combination of our
two distance results, and highlight the importance of using complementary
distance estimations to safeguard against the pitfalls of any single approach.
We conclude that the methodology presented in this work is a promising way to
determine distances to gas emission features in Galactic plane surveys.
