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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.