The Structure-Activity Relationships (SAR) landscape and activity cliffs concepts have their origins in medicinal chemistry and receptor-ligand interactions modelling. While intuitive, the definition of an activity cliff as a "pair of structurally similar compounds with large differences in potency" is commonly recognized as ambiguous. This paper proposes a new and efficient method for identifying activity cliffs and visualization of activity landscapes. The activity cliffs definition could be improved to reflect not the cliff steepness alone, but also the rate of the change of the steepness. The method requires explicitly setting similarity and activity difference thresholds, but provides means to explore multiple thresholds and to visualize in a single map how the thresholds affect the activity cliff identification. The identification of the activity cliffs is addressed by reformulating the problem as a statistical one, by introducing a probabilistic measure, namely, calculating the likelihood of a compound having large activity difference compared to other compounds, while being highly similar to them. The likelihood is effectively a quantification of a SAS Map with defined thresholds. Calculating the likelihood relies on four counts only, and does not require the pairwise matrix storage. This is a significant advantage, especially when processing large datasets. The method generates a list of individual compounds, ranked according to the likelihood of their involvement in the formation of activity cliffs, and goes beyond characterizing cliffs by structure pairs only. The visualisation is implemented by considering the activity plane fixed and analysing the irregularities of the similarity itself. It provides a convenient analogy to a topographic map and may help identifying the most appropriate similarity representation for each specific SAR space. The proposed method has been applied to several datasets, representing different biological activities. Finally, the method is implemented as part of an existing open source Ambit package and could be accessed via an OpenTox API compliant web service and via an interactive application, running within a modern, JavaScript enabled web browser. Combined with the functionalities already offered by the OpenTox framework, like data sharing and remote calculations, it could be a useful tool for exploring chemical landscapes online.