Aims: The purpose of this work is to better understand the confidence limits of the photospheric solar oxygen abundance derived from three-dimensional models using the forbidden [OI] line at 6300 Å, including correlations with other parameters involved. Methods: We worked with a three-dimensional empirical model and two solar intensity atlases. Bayesian inference was employed as a tool to determine the most probable value for the solar oxygen abundance given the model chosen. We considered a number of error sources, such as uncertainties in the continuum derivation, in the wavelength calibration and in the abundance/strength of Ni. Results: Our results show correlations between the effects of several parameters employed in the derivation. The Bayesian analysis provides robust confidence limits taking into account all of these factors in a rigorous manner. We obtain that, given the empirical three-dimensional model and the atlas observations employed here, the most probable value for the solar oxygen abundance is log (ɛO) = 8.86 ± 0.04. However, we note that this uncertainty does not consider possible sources of systematic errors due to the model choice.