Paris Jackson posted this video of herself and Prince goofing around, dancing to Notorious B.I.G.'s "Juicy."

Here's what's so cool about this video -- Michael Jackson was famously protective of his kids' privacy ... covering their faces in public and almost NEVER revealing family moments like this.

Paris included a sweet message to her big brother and "role model," telling him ... "No matter where we are in the world and in life, my home is with you and the little guy. i love you so much, gooko. i’m so proud of you. happy birthday."