Supposititious is a fancy word for "based on guesswork." The word is most often used in a legal sense. If a piece of evidence is supposititious, then it's basically hypothetical. It doesn't have any hard facts to back it up.
As the sound of the word suggests, supposititious is related to the more common supposition, meaning something uncertain or unconfirmed. Supposititious also has a slightly different and less common meaning of something that has been substituted illegally for something else. If you ask for Champagne in a bar and you get a glass of sparkling white instead, that is truly one supposititious beverage.