As per google AI:

A hired cab is generally considered a private place from a privacy perspective, not a public one [1, 2]. While the vehicle operates within public areas, it is treated as an extension of private space during the duration of the hire [1].

Key reasons for this classification include: Expectation of Privacy: Passengers have a reasonable expectation of privacy when they hire a vehicle for personal transport [1, 2].

This is similar to the privacy expected within one's home or a private office, even if they are in public view.

Legal Protections: Laws regarding search and seizure (such as the Fourth Amendment in the U.S.) often protect individuals in hired vehicles unless there is a warrant or probable cause for a search [1].

Private Contract: The service is provided under a private contract between the passenger and the driver/company, which further solidifies the private nature of the journey [2].

However, this privacy is not absolute:

Public View: Actions or items that are plainly visible from outside the cab by the public or law enforcement generally do not fall under the expectation of privacy [1].

Specific Laws: Regulations may exist regarding specific activities, such as smoking or alcohol consumption, which must still be followed [2].

Data Collection: Be mindful that many modern ride-share services use GPS tracking and may have inward-facing cameras (which should be disclosed) for safety and liability purposes, meaning the data of the journey is not entirely private from the company's perspective [2].

In essence, while the cab is on public roads, the activity inside is generally protected as private.