RETIRED ADM. MICHAEL ROGERS, former director of the National Security Agency, has been cooperating with the Justice Department’s probe into the origins of the counterintelligence investigation of the Trump presidential campaign’s alleged ties to Russia, according to four people familiar with Rogers’s participation. Rogers has met the prosecutor leading the probe, Connecticut U.S. Attorney John Durham, on multiple occasions, according to two people familiar with Rogers’s cooperation. While the substance of those meetings is not clear, Rogers has cooperated voluntarily, several people with knowledge of the matter said. Rogers, who retired in May 2018, did not respond to requests for...