Arthur Conan Doyle devoted a whole chapter of his book The Edge of the Unknown to a detailed argument that Houdini had genuine psychic power, but wouldn’t admit it. Curiously, Doyle and Houdini remained friends for a long while, in spite of public clashes over spiritualism. Perhaps they shared an appreciation of the value of public self-promotion. Eventually Houdini became outraged as a result of a seance in which Mrs. Doyle claimed to have communicated with Houdini’s mother, and the details she reported were obviously wrong.
Here’s a video of him talking about it a few weeks before he died: