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.
If what you are experiencing is mere waswasah (obsessive doubts), then your prayer is valid in any case. We advise you to disregard such doubts and to pay absolutely no attention to them in the future. Indeed, this is the best remedy for them.
However, if they are not mere doubts, then what you mentioned - that you believe that it is most likely that you had omitted a letter while reciting the Faatihah - is considered the same as having doubts about it. Many scholars held that doubting is the same as believing that something "most likely" happened. Az-Zarkashi wrote, "Doubt according to Al-Khiraqi is the opposite of certainty, even if it amounts to believing that it is most likely (that he has done or has not done a given act) according to the jurists and Arabic linguists. This view is adopted by Al-Jawhari, Ibn Faaris, and others..." [Sharh Mukhtasar Al-Khiraqi]
The Shaafiʻi book Asna Al-Mataalib reads, "There is no difference between the case when the two possibilities are equally probable (without knowing or feeling that one is more likely than the other) or when one of the two possibilities is more likely than the other. This view was stated by An-Nawawi in his book Ad-Daqaa'iq and other books. An-Nawawi said, 'Doubt here and in most branches of Fiqh means wavering between equal probability and most-likeliness...'"
When the praying person doubts omitting a letter of the Faatihah before finishing its recitation, the basic principle is that he did not recite the Faatihah, and his prayer is invalid, according to the Shaafiʻis, if he did not correct his mistake. However, if he has such doubts after having finished the recitation of the Faatihah, then he should simply disregard the doubts, and his prayer is valid. Asna Al-Mataalib reads, "When the praying person doubts omitting a letter or more of the Faatihah after having finished reciting it, then the prayer is valid because it is more likely that he has recited it. However, if he doubts omitting one or more letters before finishing reciting it or doubts reciting it or not, then he should recite it (from the beginning) and carry on with his prayer because the basic principle in this case is that it has not been recited."
In any case, such a prayer is valid according to the scholars who hold that the person led in prayer is not obliged to recite the Faatihah in the congregational prayer (because the imaam recites it on his behalf). Ibn Qudaamah wrote, "In brief, according to Imaam Ahmad, the one being led in the prayer is not obliged to recite what the imaam recites in an audible or inaudible voice in the congregational prayer, as narrated on the authority of the group of Ahmad's students. This view was also adopted by Az-Zuhri, Ath-Thawri, Ibn ʻUyaynah, Maalik, Abu Haneefah, and Is-haaq..." [Al-Mughni] You can follow this scholarly view, especially given that the incident already took place and ended.
Allaah knows best.