Falcon 50 fractional jet crew reported a pressurization malfunction during climb to cruise altitude. The crew initiated [priority handling] descent and diverted to an alternate airport and landed safely.

Narrative

Day 0Aircraft Dassault Falcon 50; Aircraft XCaptain Person A.SIC Person B While flying enroute from ZZZ1 to ZZZ aircraft experienced a rapid cabin depressurization.Rapid depressurization of cabin occurred at approximately XA:40z; 32 minutes into flight (take off time XA:08z). Location approximately 5NM south of ZZZ2 airport. Altitude FL350+ during climb; on autopilot; with intended level off at FL360. Speed approximately M0.78. No notable thud or bang sounds heard. CABIN warning light illuminated; ears popped and cabin oxygen masks self deployed. Captain (PNF) and SIC (PF) donned oxygen masks; Captain assumed controls (now PF). Captain initiated [priority handling] descent. Captain and SIC each made [priority handling] radio calls in the blind (due to headset removal for oxygen mask donning) to center [requesting priority handling] descent. Transponder code XXXX squawked; ATC communications re-established. Clearance to 14;000 feet assigned; revised to 10;000 feet.Event communication with company established. Route change to ZZZ3 requested and received from ATC. Remainder of flight uneventful at 10;000 feet. CABIN light extinguished at XB:12. Visually flew RNAV XX approach route and landed at ZZZ3; 20:35z. Aircraft delivered and parked at maintenance facility.Flight was for purpose of repositioning; no passengers on board. Aircraft was parked outside overnight prior to flight; in rain. Water drops were noted inside Aft Compartment during pre-flight inspection.On the previous day; this aircraft was flown at flight levels; by this crew with no pressurization anomalies observed.As of Day 1. Pressurization controller suspected cause.