There is an argument between the "Rishonim" [mediaeval authorities] about the usual law that money that someone has stays where it is unless another party brings a proof. המוציא מחבירו עליו הראיה. The question is what happens if the other party grabs it after there is already raised a doubt.
See Bava Mezia page 6b and 7a.
There is a "teaching" that raises the question if a sheep or goat or cow has given birth before.  Then it gives birth. If it would be known that the calf was first born then it is given to a priest. And sacrificed.
But if there is a doubt then it stays with the owner but it can not be used for work or sheared for wool. So one one hand it is like a first born in that shearing and work are forbidden. But it is like a non first born in that the owners keep it.
The Gemara says the reason it stays with the owner is that money that someone has stays where it is unless another party brings a proof. המוציא מחבירו עליו הראיה. So if a priest would grab it it would stay by the priest. Raba says we would take it away.
[Actually what Raba meant is the very issue at hand. Rav Shach says what he actually said was that even if we would say you take it away from the priest even so it would be forbidden in work and shearing.