Something worth remember...
A conspiracy involves a group of people secretly planning together to commit an ILLEGAL act. Simply secretly planning something as a group is not a conspiracy, though we might use the word, for example "My family conspired to give my sister a surprise birthday party". While the word is used in this way, that example is not, in fact, a conspiracy.
-Gumboot
con·spir·a·cy (kn-spîr-s)
n. pl. con·spir·a·cies
1. An agreement to perform together an illegal, wrongful, or subversive act.
2. A group of conspirators.
3. Law An agreement between two or more persons to commit a crime or accomplish a legal purpose through illegal action.
4. A joining or acting together, as if by sinister design: a conspiracy of wind and tide that devastated coastal areas.
There are many definitions of conspiracy, you are just giving the legal one