Neighbourhoods of precise probabilities are instrumental to perform robustness analysis, as they rely on very few parameters. Many such models, sometimes referred to as distortion models, have been proposed in the literature, such as the pari-mutuel model, linear vacuous mixtures or the constant odds ratio model. In this paper, we show that all of them can be represented as probability sets that are neighbourhoods defined over different (pre)-metrics, providing a unified view of such models. We also compare them in terms of a number of properties: precision, number of extreme points, n-monotonicity,. .. thus providing possible guidelines to pick a neighbourhood rather than another.