In this paper, we focus on the very specificity of rumors as pieces of information for modeling their process of propagation. We consider a population of pedestrians walking in a city and we assume that a rumor is transmitted by word of mouth from one to another. Although the diffusion of a rumor is of course a multi-dimensional process driven by sociological, economical and psychological elements, in this first step, we emphasize one main dimension of this complex phenomenon only. This dimension is the neighborhood of individuals likely to spread the information. With a confrontation of two antagonistic properties of the neighborhood that are profusion and scarcity of spreaders, we highlight specific characteristics of rumors. This study could lead to the psychological mechanism involved in the decision for a person to become or not a spreader himself/herself. In summary, we study if scarcity could be the silver bullet explaining how a rumor spreads.