I've had 2 ectopic pregnancies in which my right tube was removed and a piece of left tube was removed was wondering what are my chances of conceiving naturally

OB should be able to help. Remember, there are a lot of un-adopted children, our daughter has 2!

Do you know if your left tub was joined? I think that, considering scar tissue and everything, it is unlikely that your ovulated eggs will make it to your uterus or the sperm will make it to your egg. I think you might be sterile traditionally speaking. That isn't to say that you can't get pregnant, but you'll need to use IVF. I think it is likely they'll be able to harvest your eggs and go from there.

I don't think your chances are that high at all.

Much will depend on the health of the left tube and your ovaries. If your remaining tube is healthy enough, a hsg test would be helpful in this situation, it could pick up an egg released from either ovary.

As was said, it would be wise to discuss your particular circumstances with your gynecologist, and perhaps seek a referral to a reproductive endocrinologist, to see what options you might have of possibly achieving pregnancy naturally or with assistance.