If the husband has given three talaqs and he admits it, or there are legal witnesses, then three irrevocable talaqs (mughallazah) will took place and their husband-wife relation came to an end completely. After passing iddah period you would be free to marry any man other than your husband. Your nikah with your first husband is not valid without a legal halalah.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband