Lord Vile drinks his whisky randomly, and the probability that, on a given day, he aas n glasses equals e-'/n!, n = 0, 1,... Yesterday his wife Lady Vile, his son Liddell and his butler decided to...

Extracted text: Lord Vile drinks his whisky randomly, and the probability that, on a given day, he aas n glasses equals e-'/n!, n = 0, 1,... Yesterday his wife Lady Vile, his son Liddell and his butler decided to murder him. If he had no whisky that day, Lady Vile was to kill him; if he had exactly one glass, the task would fall to Liddell, otherwise the butler would do it. Lady Vile is twice as likely to poison as to strangle, the butler twice as likely to strangle as to poison, and Liddell just as likely to use either method, Despite their efforts, Lord Vile is not guaranteed to die from any of their attempts, though he is three times as likely to succumb to strangulation as to poisoning. Today Lord Vile is dead. What is the probability that the butler did it?