well founded 
adjective
(Especially of a suspicion or belief) based on good evidence or reasons: their apprehensions were well founded...
- The doctor in charge of the case duly informed the social worker and the police of her well-founded suspicions.
- What do you mean by a well-founded suspicion if you do not simply mean a reasonable suspicion?
- A requirement that the defendant's belief be well-founded is ambiguous.
Synonyms
justifiable, justified, warranted, legitimate, defensible, supportable, sustainable, tenable, well grounded, valid, admissible, allowable, understandable, excusable, warrantable, acceptable, reasonable, logical, sensible, sound, just, bona fide, genuine, plausible, credible, believable