  We prove a large deviation principle for a sequence of point processes
defined by Gibbs probability measures on a Polish space. This is obtained as a
consequence of a more general Laplace principle for the non-normalized Gibbs
measures. We consider three main applications: Conditional Gibbs measures on
compact spaces, Coulomb gases on compact Riemannian manifolds and the usual
Gibbs measures in the Euclidean space. Finally, we study the generalization of
Fekete points and prove a deterministic version of the Laplace principle known
as $\Gamma$-convergence. The approach is partly inspired by the works of Dupuis
and co-authors. It is remarkably natural and general compared to the usual
strategies for singular Gibbs measures.
