You've applied for a higher position at your company. You had a job interview that went well, so you think you might get the job. You are telling your wife about this, and you say:
I think I have a pretty good shot at getting it.
You describe something as being "pretty good" when you think it's good, but you don't want to sound too optimistic.
To "have a shot at" a prize or reward means that your chances of winning are not bad. It means that you think there's a chance that you might win.
You can use this phrase followed by a noun:
Do you think I have a shot at the job?
Or you can follow it with "___ing":
Do you think I have a shot at getting the job?
There's also a similar phrase that's used when talking about men trying to attract women. When you think a man might be able to attract a woman, you say that he "has a shot with" her.
To "get" a job means that you're hired for it.
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