What right could you invoke to protect yourself from a police officer with no probable cause entering your house without a warrant?

In the US, the Fourth Amendment says: The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated [...] In practice, it's difficult to stop a man with a gun who breaks down your door from doing anything he wants. However, your lawyer can later argue in court that the police did not have probable cause and so anything they found in your house is inadmissible as evidence. In fact, even if they're not trying to introduce evidence found in your house at the time, but something they found because something they saw in your house lead them to it, it's still inadmissible (as "fruit of the poison tree").

Many (though not all) other countries have similar provisions, but you'll have to look up for yourself what they are.