Aims. While spreads in chemical composition are now believed to be a universal characteristic of globular clusters (GCs), not all of them display evidence of multiple populations in their color-magnitude diagrams (CMDs). Here we present a new scenario for the formation of GCs, in an attempt to qualitatively explain these otherwise elusive observational results. Methods. Our scenario divides GCs into three groups, depending on the initial mass (M I ) of the progenitor structure (PS), as follows: i) massive PSs can retain the gas ejected by massive stars, including the ejecta of core-collapse SNe. ii) Intermediate-mass PSs can retain at least a fraction of the fast winds of massive stars, but none of the core-collapse SNe ejecta. iii) Low-mass PSs can only retain the slow winds of intermediate-mass stars. The first group would contain members such as ω Centauri (NGC 5139), M 54 (NGC 6715), M 22 (NGC 6656), and Terzan 5, whereas NGC 2808 (and possibly NGC 2419) would be members of the second group. The remaining GCs that have only a spread in light elements, such as O and Na, would be members of the third group. Results. According to our scenario, the different components of ω Cen should not have a sizeable spread in age. We argue that this is consistent with the available observations. We present other simple arguments in favor of our scenario, which can be described in terms of two main analytical relations: i) one between the actual observed ratio of the number of first to second generation stars (R FG SG ) and the fraction of first generation stars that have been lost by the GC (S L ) and ii) another between S L and M I . We also suggest a series of future improvements to and empirical tests of the modeling that may help decide whether the proposed scenario properly describes the chemical evolution of GCs.