I don’t know about probable cause for a search, but legally speaking, clamming up to a specific question, as opposed to explicitly invoking the 5th amendment right, currently means something in trial, as ruled in Salinas v. Texas.

https://www.oyez.org/cases/2012/12-246

I don’t see how telling the officer you have $87k is probable cause for a search, anyway.

Isn't it a probable cause to search your car, since it's the car and the cash that has broken the law, and has no rights to privacy?

No.

First, it is not illegal to have a car or cash.

Second, in the US at least the government does recognize a limited right to privacy in the form of the 4th amendment which spies to States as well. An officer cannot search you, your car or your home without a warrant from a judge or a tangible reason to believe you are committing a crime.

Or if you agree to a search!