In which country or state? They're not all the same but I see from previous questions you are British. So I shall answer for English law, which also happens to be what I have experience of. If you are in Scotland, probate is called confirmation so I'm guessing you're not there.
The girlfriend wasn't married to him, so she's not family and gets nothing. If she sells anything or takes his money, that is theft from his estate and will be dealt with as theft. She must return what she took.
What probate does is appoint executor(s) or administrator(s) to administer the estate. As the nearest relatives, all four of you share the estate equally in accordance with the intestacy rules in the Law of Property Act 1925. And what the High Court Probate Registry will normally do is appoint all of you to be joint administrators. So you can sort it out amongst yourselves as long as you get equal value each. That's all the law says - in the absence of a will and with no surviving wife (divorce always cuts you out of your spouse's will), the kids get equal shares and there is no guidance as to who gets what. How, really, can there be? Sorry, who gets what is your own problem and if you can't agree, the only real solution is to sell everything and divide up the money equally. I hope you will all be sensible so it doesn't come to that.
The only claim an unmarried girlfriend can have on the estate in English law is if she was dependent on him. If she was living on his income so his death leaves her with nothing to live on, she can make a claim for part of his estate. Which could be expensive as the High Court Chancery Division has to deal with "contentious probate" and both sides will need a barrister. Ever read Charles Dickens's "Bleak House"? It is partly a satire on how slow and expensive the Court of Chancery was, and the Jarndyce probate case in it ends with the entire estate disappearing in legal fees. Today's High Court should be rather more efficient, we hope! But it could still be expensive if she makes a claim. Expensive for her, too, so let's hope she doesn't.
If they owned a house together as joint tenants, she automatically inherits it and it doesn't become part of the estate. What I don't know is who would pay any inheritance tax on his half, though hopefully that falls within the exemption. If they had been married, no problem as anything she gets would be exempt. (A problem when Sir Nigel Hawthorne died - because he couldn't be married to his partner Trevor and they had a big house, Trevor had to sell up and move somewhere smaller to pay the tax. Being of a similar persuasion myself, guess why we wanted civil partnership, if not marriage!)
Oh well, moral of the story... make a will! I talked through all this at length with my sister and her partner and wrote wills for them, then they eventually decided what the heck, at their age (they're both 50), let's just get wed. It'll save on inheritance tax and Mum's happy now she has a granddaughter by marriage as my brother-in-law's son from his previous relationship had a baby last year with his girlfriend....complicated, innit?
I did my Dad's probate without a solicitor and read a thing or two on the way.