Lady Macbeth (in the Scottish play which, aptly, is at the center of the plot) uses this phrase while babbling insanely out of GUILT for her role in a murder.
(Rough paraphrase, from memory):
"Is this a dagger that I see, the handle toward my hand? Or art thou but a dagger of the mind?"
(Lady Macbeth is NOT holding a dagger, and has no real blood on her hands -- she is hallucinating, from guilt)
So, the "Columbo" ending has nothing to do with the real-life likelihood of the bead lodging in the umbrella. As in the best "Columbo" plots, it's all about Columbo's innate mastery of psychology -- in this case, his ability to skilfully drive a guilt-ridden killer over the edge, just like Lady MacB.