Did not Abraham have prior experiences under which he could pin his faith?
What can I tell you except to say that 'faith' in a philosophical perspective, is taken to be something that lacks 'strong evidence', in an empirical or scientific sense.
This basis of prior experience you mention is actually reasoning.
If C follows A+ B today, shall I assume it will tomorrow? Maybe, maybe not.
Is reasoning a type of 'scientific evidence'? Not unless supported by other things, predictions that come about, for example. Other lines of reasoning, with other premises, that yield the same results. Even then it may be considered weak evidence.
In the case of the Bible, the recurring theme on this is of the nature that unbelievers lack faith and want evidence. Thomas did not believe, wanted 'evidence'.
 The other disciples therefore said unto him, We have seen the Lord. But he said unto them, Except I shall see in his hands the print of the nails, and put my finger into the print of the nails, and thrust my hand into his side, I will not believe.
 And after eight days again his disciples were within, and Thomas with them: then came Jesus, the doors being shut, and stood in the midst, and said, Peace be unto you.
 Then saith he to Thomas, reach hither thy finger, and behold my hands; and reach hither thy hand, and thrust it into my side: and be not faithless, but believing.
 And Thomas answered and said unto him, My Lord and my God.
 Jesus saith unto him, Thomas, because thou hast seen me, thou hast believed: blessed are they that have not seen, and yet have believed.
Do you expect evidence, or are you blessed?
Also these reminders, that evidence is not required by the faithful:
 Wherefore, if God so clothe the grass of the field, which to day is, and to morrow is cast into the oven, shall he not much more clothe you, O ye of little faith?
 And he saith unto them, Why are ye fearful, O ye of little faith? Then he arose, and rebuked the winds and the sea; and there was a great calm.
 And immediately Jesus stretched forth his hand, and caught him, and said unto him, O thou of little faith, wherefore didst thou doubt?
 Which when Jesus perceived, he said unto them, O ye of little faith, why reason ye among yourselves, because ye have brought no bread?
 If then God so clothe the grass, which is to day in the field, and to morrow is cast into the oven; how much more will he clothe you, O ye of little faith?
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Your position is of the nature 'I have reason for my faith.'
In a broad sense, experience leads you to believe what you hold to be true. On any particular issue, no real 'convincing evidence', but many experiences that have convinced you.
The greatest proof any of us can have for our own beliefs is experience.
If you 'know', beyond any reasonable doubt, that you have ridden on a spaceship with aliens, no further evidence is required, for you to believe. Others will scoff, and say 'Show us the evidence.', but you have none except your own experience.
For you, this is sufficient. For others, they must accept it on faith. If they know by a lifetime of living with you, that you are a truthful person, not delusional, not one to fabricate stories, serious as a heart attack day in and day out, still, on this one issue, they must have faith to believe.