Let \(\Gamma\) be a topological groupoid with contractible object space X such that source and target maps are local homeomorphisms. Let \(S(\Gamma)\) be the discrete monoid of sections s: \(X\to\Gamma \) of the source map \(\Gamma\to X\). The main theorem of the paper states that \(B\Gamma\), the classifying space of \(\Gamma\), is weakly homotopy equivalent to the classifying space of certain submonoids of \(S(\Gamma)\). In the proof of this theorem also a weak homotopy equivalence between the loop space of the classifying space of some topological categories (categories with simplified fractions) and the geometric realization of a simplicial group is constructed. The main examples are classifying spaces of foliations.