Contingent Liability. Definition: A contingent liability is either a possible obligation arising from past events and depending on future events not under an entity's control, or a present obligation not recognized because either the entity cannot measure the obligation or settlement is not probable.ontingent Liability. Definition: A contingent liability is either a possible obligation arising from past events and depending on future events not under an entity's control, or a present obligation not recognized because either the entity cannot measure the obligation or settlement is not probable.