My son is on probation, and his oo showed and searched his place. Did he have the right to go through his wife's personal stuff. Like her bureau drawers?

What is 'oo' first off; did he have a search warrant and what was he looking for? If he had a search warrant he could look anywhere he wanted to.

If you mean PO, they don't have to distinguish one person's storage from another's in the same household.
He or she should be asking questions about their rights because too much gets lost second hand.

Yes I meant po. What do you mean about asking questions. Please elaborate. Also, does his wife have to abide by the same rules, like have a drink or have alcohol in the home?

I mean he's not here to say what his PO has told him about unannounced visits, searches, and violations.
Again, a PO can't and doesn't have to try to distinguish between one place or member of a house. A wife may have all the rights in the world as any free person does, but if she shares a house with him, she can't just declare what is his and what is hers. The PO can assume otherwise and the law will back him. He can't stuff drugs in his kid's teddy bear, or say that booze in the kitchen belongs to his wife, or the gun in his dad's bedroom nightstand is OK because it's registered to his dad. He can't BE in that house, near anything that violates his terms, and if his living quarters can be searched, then that includes the whole place.