CRJ900 Captain reported right bleed duct warning with pressurization failure resulted in expeditious descent and divert to nearest airport.

Narrative

We were operating flight ZZZ to ZZZ1 after a two hour delay and maintenance issue (Slat Fault). The first officer was flying while I; the captain; was pilot monitoring. We had departed ZZZ and climbed up to FL270. Between about FL200 and FL270 we had been in an out of clouds with temperatures below 10 degrees Celsius; and had received ICE cautions; so we turned on the Wing and Cowl Anti Ice. We had only been at FL270 for a short time when we received a R BLEED DUCT warning message. We both watched the warning for a few seconds then I began to pull out the QRH. I knew that the bleed duct affected the anti-icing system so I asked ATC for a descent to 15;000 ft to exit possible icing conditions. While they were working on my request; I began to read the QRH Caution message. The message stated that all bleed air sources would close; resulting in a loss of pressurization. I switched to the ECS (Environmental Control System) to determine if both engine bleed valves had closed. At this point ATC had granted our request for 15;000 ft and the FO (First Officer) had begun a descent from FL270. I checked the cabin pressure and noted that the pressure had already risen to 6;800 ft pressure altitude; less than a minute or two before it had been at around 4;000 ft. I asked ATC for 10;000 ft and was told they could only bring the airplane down to 13;000 ft. After a brief discussion with the FO about the Cabin Alt Caution and Warning that would be coming soon; I [requested priority handling] and let them know we would be going to 10;000 ft. While descending; we did not want the cabin altitude to reach 14;500 ft which would have deployed the passenger oxygen masks. The FO and I decided to do an expeditious descent as the cabin altitude continued to climb fairly quickly. We performed the descent checklist and proceeded down to 10;000 ft. At this point I sent a message to Dispatch via ACARS and let them know we had a R BLEED DUCT warning; [requested priority handling]; and performed an expeditious descent. I was searching my charts for a suitable airport and any help on a suitable destination would be welcome. I then continued to perform the QRH for the R BLEED DUCT while the FO took over the rest of radio communications. While completing the QRH procedure; dispatch sent a message to proceed to ZZZ2. After completing the QRH I proceeded to the unpressurized flight procedure and completed that QRH as well while the FO loaded our flight plan direct to ZZZ2. I finally had time to call the flight attendants and make them aware of [the situation]. I then made a PA that we had an issue with our pressurization system and were diverting to ZZZ2. I called dispatch on commercial radio just to verify there was nothing else we could be doing at the time. We maintained around 300 KTS airspeed to keep the aircraft from getting too warm in an unpressurized state; then slowed to 250 for descent and proceeded the rest of the way to ZZZ2 without any more incidents. There were no injuries; nor was I made aware of any complaints by passengers while in ZZZ2.Bleed leak caused a R BLEED DUCT warning resulting in the loss of all pressurization on the aircraft at FL270. Losing pressurization quickly and knowing the CABIN ALT caution and warning were imminent lead to an expeditious descent.No real suggestions. I do wonder if the MEL Procedure for the Slat Fault could have caused something to come loose but that is all.