A method for operating an exhaust system including at least one oxidation catalytic converter, at least one configuration for selective catalytic reduction and at least one measuring probe for determining the effectiveness of the configuration, includes at least determining a conversion effectiveness of the configuration using the at least one measuring probe and calculating an effectiveness of nitrogen monoxide conversion in the oxidation catalytic converter from the determined conversion effectiveness. In this way, an estimate of the effectiveness of the nitrogen monoxide conversion to nitrogen dioxide of an oxidation catalytic converter in the exhaust system can be obtained without additional measuring probes in or on the oxidation catalytic converter. This reduces the maintenance frequency of the exhaust gas system and at the same time enables precise regulation of the exhaust gas conversion as a whole. An exhaust system and a vehicle having an exhaust system are also provided.