I was quoting the speaker in the video; however, based on the following:
Originally Posted by Nightmare
Having the effect of proof, tending to prove, or actually proving.
When a legal controversy goes to trial, the parties seek to prove their cases by the introduction of evidence. All courts are governed by rules of evidence that describe what types of evidence are admissible. One key element for the admission of evidence is whether it proves or helps prove a fact or issue. If so, the evidence is deemed probative. Probative evidence establishes or contributes to proof.
Probative facts are data that have the effect of proving an issue or other information. Probative facts establish the existence of other facts. They are matters of evidence that make the existence of something more probable or less probable than it would be without them. They are admissible as evidence and aid the court in the final resolution of a disputed issue. For example, in the case of a motor vehicle accident, a witness's testimony that she saw one automobile enter the intersection on a red light is a probative fact about whether the driver was at fault.
... it seems to me that an officer asking "probing" questions is seeking to establish "Probative facts [that] establish the existence of other facts" that would lead to other actions including search, seizure or arrest. I have no problem with using the word "probative," especially since it has a legalistic meaning and because the officer probably does not understand what the word is.
If you don't like the use of that word, feel free to use some other word.