Our goal is to establish a mathematical framework suitable for the description of geographical distances related to movement in space and produced by transport means. We propose to root the idea of effort --or disutility-- minimisation into the definition of geographical distance and its mathematical formalisation. This objective is non-trivial to achieve because of the issue of possible triangle inequality violation due mainly to the need for break in any movement. This issue translates into additivity problems that may disturb the order of proximities in geographical spaces, and undermine their basic geometrical properties. In order to address this issue, we introduce the concept of contextual distances that, in parallel to pure geometric movement, considers a context where resources used to move are accounted for, that it be time, money or other relevant quantities. We show that contextual distances follow some of the properties of metrics. In particular contextual distance respects the triangle inequality. This result paves the way for its use within the context of spatial analysis in geography.