"It's less probable, but it's still possible," Brailsford told Cyclingnews after stage 17 had seen all the top four favourites finishing close together in the Mas de la Costa climb, and when asked if he believed victory in Madrid was still a realistic option for Chris Froome.
"We're still on it, and the thing about Chris Froome is he's the biggest fighter I've ever come across.
"You've got to believe in it, because if you don't believe in it, it won't happen. You have think it's possible and you play your cards thinking 'right, I'm going to do this."
Reviewing the ascent to Mas de la Costa, where Sky's Leopold König was narrowly defeated in the stage win battle and Froome was able to resist attacks by Alberto Contador (Tinkoff) behind by using his usual pacing strategy for climbs, Brailsford argued, "I think there were two races and it's a real disappointment for Leo who I thought paced the climb fantastically well and just cut it a little bit short there at the end there.
"But equally for the gc guys, it was one of the toughest climbs of the Vuelta and on those types of climbs there's not so much tactics as race for survival.
"Chris once again showed his mental strength in letting them go a little bit, coming back to them, letting them go, knowing full well he'd be able to close it in the end."
"He's probably unique in that sense in cycling in the way he rides, everybody thinks he's in trouble and the way he comes back on them - the mental tenacity, the strength, the discipline to be able to do that - is incredible.
"From a race point of view, Chris, Contador and Chaves all close together on the podium and that, seems to be a more intricate race, Nairo didn't look to be in difficulty.
"But that race for the podium looks very open and interesting, so we'll get the next (Thursday's) stage done, do the time trial and then go from there."
Looking ahead to Friday's time trial, Sky have always believed it will be a crunch moment in the outcome of the race and with Froome looking to make up time on Quintana and distance his rivals behind him, even more so.
Predicting exactly how it will go, Brailsford was cautious, pointing out that time trials, particularly ones of this length in a third week when riders are no longer fresh were difficult to predict. On top of that, the Calp time trial is reportedly a real mixture of technical sections and long, flat, straight sections.
"It's not a straightforward one, normally pace management is the key and the great time triallists - Chris, Tony Martin, Bradley [Wiggins], [Fabian] Cancellara - are all masters of pacing. But when you add in the technicality of the roads and the nature of the roads, it becomes an extra challenge, it'll be a real test of skill, technical ability and tactical ability but as always, and above all, it's a test of mental strength."