TWo things come to mind when considering this for me:
1.The rule of reciprocity would suggest that I reverse the roles, and consider what I would want someone to do if they bought the item off of me. Or I could even make it entirely impersonal, and look at what seems fair with two other people. Both lead me to thinking that splitting it half-and-half would be fair
2. But then’s there’s a different consideration: if I told them before buying it, would they agree to split it with me in the same way? Probably not. Sure, under capitalism you can buy something for what someone will sell it for, but it’s not like that’s always ethical. If you tricked someone into thinking something was worth little money, that would be unethical. If they tricked you into paying more than something was worth, that would be unethical.
And there’s an argument that they are not giving their informed consent to selling the item.
Ultimately, I think that I would do number 1, but the reason would be selfish, and not moral. I would want the money, and then I would want assuage my guilt by splitting it with them after the fact.
That is, leaving out the issues of them trying to sue me to get it back or something. I’m assuming here that the price is high enough that they’d rather get half than risk not only getting none but being out the legal fees. I’m also assuming they’re not a horrible person, and that they’re of about equal in wealth as me.