When using convex probability sets (or, equivalently, lower previsions) as uncertainty models, identifying extreme points can help simplifying various computations or the use of some algorithms. In gen-eral, sets induced by specific models such as possibility distributions, lin-ear vacuous mixtures or 2-monotone measures may have extreme points easier to compute than generic convex sets. In this paper, we study ex-treme points of another specific model: comparative probability order-ings between the singletons of a finite space. We characterise these ex-treme points by mean of a graphical representation of the comparative model, and use them to study the properties of the lower probability in-duced by this set. By doing so, we show that 2-monotone capacities are not informative enough to handle this type of comparisons without a loss of information. In addition, we connect comparative probabilities with other uncertainty models, such as imprecise probability masses.