Grumbler, this is more like chances of SURVIVAL, COMING OUT OF A SITUATION UNSCATHED, SAFETY

Здесь речь идет не об опасности, а об отношении к лифтам вообще - "I started down the stairs ... I rarely use the elevator ... I don't trust machines".
Не знаю, как лучше перевести....

Шансы спуститься без проблем по лестнице мне нравились больше, чем ...

If he takes the stairs because he doesn’t trust machines, that means that he fears for his safety, no? He’s afraid something can happen to him on the elevator and his odds for safety are better on the stairs.

Спуск по лестнице казался мне более безопасным, чем в лифте с его ограниченным пространством. ¿

That sounds more like what I was thinking.

So my translation is based on what you were thinking. 😉

Мои шансы уцелеть, спускаясь по лестнице казались мне выше, чем при спуске в лифте с его ограниченным пространством.

"безопасность" и особенно "уцелеть" звучат как угроза для жизни или хотя бы здоровью. Человек просто не доверяет лифтам и не хочет застрять.

“I started down the stairs. I rarely use the elevator, even though I’m on the fifth floor. Like I said, I don’t trust machines. They’re always breaking down on me just when I need them. Besides which, if I were someone in this town using magic to kill people two at a time, and I DIDN’T WANT TO GET CAUGHT [= survival], I’d make sure that I removed the only practicing wizard the police department kept on retainer. I LIKED MY ODDS ON THE STAIRWELL a lot better than I did in the crumpled confines of the elevator. Paranoid? Probably. But just because you’re paranoid doesn’t mean that there isn’t AN INVISIBLE DEMON ABOUT TO EAT YOUR FACE.” [=the whole passage is about surviving dangerous odds and things threatening him]