All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
What should be taken into account is the waiting period ('Iddah). If your ex-husband did not embrace Islam until your waiting period expired, then it becomes permissible for you to marry another man. Please refer to fataawa 107894 and 84226.
It is a condition for the validity of the marriage contract that it be conducted with the presence and consent of the bride's guardian (Wali) and the presence of (two) witnesses.
If a woman does not have a Muslim guardian, then it is the Muslim ruler who marries her off. If there is no Muslim ruler, then she appoints a trustworthy Muslim man to marry her off. Please, refer to fatwa 88488.
Therefore, if the marriage was conducted fulfilling the conditions of a valid marriage underlined in fatwa 83629, then it is a valid marriage. However, if one of the conditions of marriage was not fulfilled, like, for example, if it was conducted without the presence and consent of the guardian, then it is a void marriage according to the preponderant opinion of the jurists (scholars) and it must be annulled.
If the marriage was conducted while you were still in your waiting period from the first husband, then it is a void marriage. So you must separate from him [i.e. from your current Muslim husband] if that is the case. If both of you wish to continue your marital life, then you must renew the marriage contract while fulfilling the conditions of a valid marriage.
As for calling your first husband to Islam and the divorce proceedings, then all this does not have any effect on your marriage with the Muslim man if that marriage was conducted in accordance with the Islamic rulings.
Allaah knows best.