1) Affording proof or evidence 2) Exploratory 3) Important 4) Significant 1) Significant 
adj. in evidence law, tending to prove something. Thus, testimony which is not probative (does not prove anything) is immaterial and not admissible or will be stricken from the record if objected to by opposing counsel.
• (a.) Serving for trial or proof; probationary; as, probative judgments; probative evidence.
It means the tending to prove or actually proving something. In the court of law, evidence is a must, without which, the defence have right to request for the dismissal of case and the court would do so. So any evidence brought in has to be probative otherwise it would not hold any value in court of law.
Pro'ba·tive adjective [ Latin probativus : confer French probatif .] Serving for trial or proof; probationary; as, probative judgments; probative evidence. South. 
Tending to prove something. Courts can exclude evidence that is not probative (does not prove anything).
[adj] - tending to prove a particular proposition or to persuade you of the truth of an allegation
probatory adjective tending to prove a particular proposition or to persuade you of the truth of an allegation; `evidence should only be excluded if its probative value was outweighed by its prejudicial effect`
serving or designed for testing or trial. · affording proof or evidence.