Especially if you are applying for funding, the admissions committee is taking a risk when they decide to admit each student. If a student comes and does not succeed, the department may have incurred expenses for the time the person was there, and they don't have another successful graduate they can show for it. Is the reason you dropped out before something that still affects your likelihood to drop out again? That'll be a question on the committee's mind as they're reading.
Having been expelled before would be a bigger issue, because it means you were a major problem for the previous place and most universities don't want to have people who they think would be likely to cause big problems like that for them. An applicant with this background would definitely be expected to explain what's changed.
Some departments expect a certain percentage of students to be "weeded out" or not make it through; find out what the norm is where you're applying. Also find out what the culture is in terms of encouraging people to branch out and try new things, but then be able to recognize when something's not working out and stop going down a path that doesn't lead to fruitful goals (once that's recognizable). These are important parts of research, and I think most faculty understand that.
In your applications, clearly explain what happened, and how you made the most of it. Is the experience you gained an asset that can help you now? Also (this applies more broadly) explain why you want to now go back into academia and into the program you're applying for and why you think you'll be able to make the most of that opportunity, if admitted.
If you just assume your history makes you ineligible and don't apply, you won't be admitted.
If you do apply and explain things clearly, you have a chance, higher than zero.