Depends on if those countries have extradition treaties with each other, and possibly some other factors that vary by country.
For instance, there was a guy who murdered a woman in the Philadelphia area and fled to France. He was convicted in absentia and sentenced to death, but France would not extradite him because of the death penalty (I think).
Edit: If you are given asylum, that means they will not extradite you. But being given asylum is not common and it is not the same thing as simply being allowed into the country.