Conocchia made his film debut in 1960 with Federico Fellini 's La Dolce Vita , playing the part of a lawyer.

Three years later, he worked again with Fellini, for 8½ , a film where he had a good part, that of the production inspector at the service of the protagonist Marcello Mastroianni . In the film he was dubbed by Mario Carotenuto .

In 1965 he took part in the film Giulietta degli spiriti , again in the role of a lawyer. Seven years later he lent his voice to Gore Vidal , for the film Roma . The last film in which he took part was Ginger and Fred .

He was the father of the voice actress Luisella Visconti , who died prematurely in 1967.