Synthetic progesterone is progesterone.
Finasteride just 'poisons' the the enzyme responsible for attaching two hydrogen atoms to suitable hormones. Progesterone like testosterone can be reduced by the same enzyme to DHP and DHT respectively.
The drug does not behave like a hormone, it does not act as an androgen or estrogen but resembles them sufficiently enough to bind to and deactivate the 5aR enzyme.