Algol is right on both accounts, Houdini was an only child and was devastated at the loss of his mother, especially as he was away on one of his world tours at the time.
It was his good friend Sir Arthur Conan-Doyle (Sherlock Holmes author) a keen spiritualist that suggested that he contacted a medium.
Just like Randi, being a magician he could see instantly that these mediums were using simple conjuring tricks to extort money from often bereaved and gullible people, he didn't give up though he went to another and another but never found a genuine one, he then spent the rest of his life debunking fake mediums all over the world during his magic tours.
Interestingly he told his wife long before his untimely death, that when he did eventually die she would be inundated by messages from these debunked mediums saying that they had talked to him in the spirit world and that he was very sorry for what he had done to them while alive, and that they were right after all.
Houdini however, open minded to the last, gave her a code word, and said that if any medium came to her with a message from him they would use this code word first.
As you might expect, when he did die, all these debunked nediums crawled out of the woodwork with the messages that Houdini had predicted, NOT ONE knew about the code word.
I've met James Randi and he is amazing, he performed the Uri Geller spoon bending trick in front of my nose and I couldn't see how he did it, thankfully he is carrying on where Houdini left off, he's been looking worldwide for a genuine one for the past 60 years.
The application form for his challenge is unambiguous and quite clearly followed for those who thinks his challenge is not genuine.
Any 'genuine' mediums out there who don't like our answers, here's the details for you.
http://www.randi.org/site/index.php/1m-challenge/challenge-application.html
EDIT: Randi is not the judge MS, have the decency to read rule 6 in my link before going in for puerile personal attacks.
EDIT2:There are plenty of other similar organisations around the world that offer similar (if not as generous) prizes, with similar conditions, are they all liars also?
https://answersrip.com/question/index?qid=20100702043449AARQuPk&show=7#profile-info-AA10631668