A classic illustration of how to use (and how to not use) conditional probabilities:

"'Her foot,' says the journal, 'was small- so are thousands of feet. Her garter is no proof whatever- nor is her shoe- for shoes and garters are sold in packages. The same may be said of the flowers in her hat. One thing upon which M. Beauvais strongly insists is, that the clasp on the garter found had been set back to take it in. This amounts to nothing; for most women find it proper to take a pair of garters home and, fit them to the size of the limbs they are to encircle, rather than to try them in the store where they purchase.'

Here it is difficult to suppose the reasoner in earnest. Had M. Beauvais, in his search for the body of Marie, discovered a corpse corresponding in general size and appearance to the missing girl, he would have been warranted (without reference to the question of habiliment at all) in forming an opinion that his search had been successful. If, in addition to the point of general size and contour, he had found upon the arm a peculiar hairy appearance which he had observed upon the living Marie, his opinion might have been justly strengthened; and the increase of positiveness might well have been in the ratio of the peculiarity, or unusualness, of the hairy mark. If, the feet of Marie being small, those of the corpse were also small, the increase of probability that the body was that of Marie would not be an increase in a ratio merely arithmetical, but in one highly geometrical, or accumulative. Add to all this shoes such as she had been known to wear upon the day of her disappearance, and, although these shoes may be 'sold in packages,' you so far augment the probability as to verge upon the certain. What, of itself, would be no evidence of identity, becomes through its corroborative position, proof most sure. Give us, then, flowers in the hat corresponding to those worn by the missing girl, and we seek for nothing farther. If only one flower, we seek for nothing farther- what then if two or three, or more? Each successive one is multiple evidence- proof not added to proof, but multiplied by hundreds or thousands. Let us now discover, upon the deceased, garters such as the living used, and it is almost folly to proceed. But these garters are found to be tightened, by the setting back of a clasp, in just such a manner as her own had been tightened by Marie shortly previous to her leaving home. It is now madness or hypocrisy to doubt. … But it is not that the corpse was found to have the garters of the missing girl, or found to have her shoes, or her bonnet, or the flowers of her bonnet, or her feet, or a peculiar mark upon the arm, or her general size and appearance- it is that the corpse had each and all collectively.

--Edgar Allan Poe, "The Mystery of Marie Roget"