To apply for the job my colleague needs?

[CrossCountryWoosh]

This sounds really arrogant and obviously Alice's application and interview might blow mine out of the water.

A colleague I really like (Alice) and I have both seen a job. Alice is applying for it and I am thinking of. We both have a really good chance of getting it. We both earn about the same. Jobs like this dont come up much.

Alice's husband is a dick. The pay rise with the new job would give her the option to leave (she doesnt feel finamcially able to right now) or at the very least give her a bit of power back.

Alice is actively looking for a new job.

I'm happy enough in my current job and wasnt looking.

So I guess, Alice needs this job and it has the potential to be life changing for her. Whereas Im thinking "that'll be fun" and "more money for shoes".

Alice wont hold a grudge if I apply or get the job. I wont hold a grudge if she gets it and doesnt make any life changes.

Obviously, her application and interview might not even give me a chance.

Should I apply and accept if I am successful?

YANBU - all is fair in love and job applications
YABU - dont potentially ruin her chance. That makes you more of a dick than her husband.

Dont come at me for my arrogance, Im just trying to think of all the possible results.

Difference of opinion. Yours is no more accurate than mine is.

Also, I have many, many friends - not that I need to justify your meritless statement with a response.

Ive decided to give it a miss.
I know Alice might not get it anyway. I also know she might get it and not make changes to her life but at least she will have the opportunity.
I hate the idea of purposely trying to stop her improving her life especially when its something that isnt that important to me.
Of course, the other applicants might be in a much worse situation than her but I dont know them.

Im very much about keeping private life and work life separate but it doesnt mean I cant like my colleagues or wish them well. We are in different parts of the country and Im under no illusions that when one of us moves on we won't stay in contact.

Not arrogant at all — you're just being honest about your own motivations, which is more self-aware than most people manage.
Here's the thing though: you can't actually give Alice this job. All you can control is whether you apply. If you don't apply, that doesn't guarantee Alice gets it — there could be other candidates, and she might not be the strongest one on the day regardless of you. So "don't apply" isn't really "give Alice a life-changing opportunity," it's "remove one competitor from a field you don't control the rest of." That's worth sitting with, because it changes the moral weight of the decision.
A few things that might help you think it through:
It's not your job to manage Alice's life circumstances. Her situation with her husband is genuinely hard, and it's completely understandable that you feel for her. But that's a reason to support her as a friend — not a reason to sideline your own career choices. If the situation were reversed, would you want Alice to hold back because your reasons for wanting it were less dramatic than hers? Probably not — you'd want her to make her own decision and let the process play out.
You said it yourself: neither of you will hold a grudge. That's actually the important bit. If you'd said Alice would be devastated or your friendship couldn't survive it, that's a different calculation. But you don't think that's true — you think you both know that applying for the same job is just... applying for the same job.

Withdrawing might not even be the kind thing to do. If Alice found out later that you didn't apply because you didn't think you should compete with her for something she needed more — how would that sit with her? Some people would feel touched. Others would feel patronised, like you'd decided her need was greater than her right to win fairly. You know Alice; only you can judge which she'd be.
A middle option: you could be honest with her. Something like "I'm thinking of applying too, but honestly you want/need this more than I do — I don't want it to be weird between us." That's not the same as withdrawing, and it's not making the decision for her, but it opens the door for her to say "please don't" or "honestly, go for it, may the best woman win" — and then you're deciding with information instead of guessing.
Ultimately: apply if you want the job. Best candidate gets it. That's not being a dick, that's just how job applications work — and it sounds like Alice, of all people, would agree.