WASHINGTON—The Supreme Court is declining to take up the case of former New York Assembly Speaker Sheldon Silver, who is serving a 6 1/2-year prison sentence after being convicted in a corruption case. The high court on Monday declined to take up the Democrat’s appeal. Once one of the three most powerful state officials, Silver was ousted as speaker in 2015 and was convicted later that year. His original conviction was overturned on appeal, but he was convicted again in 2018. Part of that conviction was then tossed out on another appeal, leading to yet another sentencing in July 2020. Silver, who’s 76, began serving his sentence in August 2020. In the part of the case that survived the appeal process, Silver was convicted in a scheme that involved favors and business traded between two real estate developers and a law firm. Silver supported legislation that benefited the developers. The …