Given a discrete-time linear switched system Σ(A) associated with a finite set A of matrices, we consider the measures of its asymptotic behavior given by, on the one hand, its deterministic joint spectral radius ρd(A) and, on the other hand, its probabilistic joint spectral radii ρp(ν,P,A) for Markov random switching signals with transition matrix P and a corresponding invariant probability ν. Note that ρd(A) is larger than or equal to ρp(ν,P,A) for every pair (ν,P). In this paper, we investigate the cases of equality of ρd(A) with either a single ρp(ν,P,A) or with the supremum of ρp(ν,P,A) over (ν,P) and we aim at characterizing the sets A for which such equalities may occur.