SHANGHAI—With the conviction of former security chief Zhou Yongkang, China’s top antigraft officials appear to have a new aim: dialing down public expectations.

Official media Friday gave muted coverage to the conviction of Mr. Zhou, once one of the Communist Party’s top leaders, on charges of bribery, abuse of power and sharing state secrets, according to official media accounts Thursday. He was the most senior Chinese political figure prosecuted for crimes since the 1970s.

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