S08E02 - Lord Edgware Dies

Jane Wilkinson, an actress, is suspected of murdering her husband, the fourth Baron Edgware, so that she can marry the Duke of Merton. The plot begins with Jane asking Poirot to convince her husband to agree to a divorce. When Poirot reluctantly does so, Edgware says that he has already agreed to a divorce and written a letter to Jane informing her of the fact. When Poirot reports this to Jane, she denies ever having received such a letter.
On the night of the murder, Wilkinson supposedly goes to the Edgware house, announces herself to the butler, and goes into her husband's study. The next day, Lord Edgware is found murdered and Chief Inspector Japp tells Poirot all about it. But in that morning's newspaper, they discover an article about a dinner party that was held the previous evening where Jane Wilkinson was reportedly a guest.
At the party, there were thirteen guests at the dinner table. One guest mentioned that thirteen people at table means bad luck for the first guest to rise from the table (hence the alternative title of the book Thirteen At Dinner) and Jane Wilkinson was the first to rise. Among the guests is a writer named Donald Ross, who spent a lot of the evening speaking with Jane. So the police are, at first, baffled with the case, as is Poirot.