It would be like picking a number between 1, 2, 3, and 4 and having a stranger guess what it is. Then picking again and having the stranger guess again. Then repeating the process for a total of 37 times and the stranger only guessing right once. Although it would be improbable it is not impossible.
I also think your math might be off but I'm not smart enough to figure out what the right math is. In a het to het breeding...
1 albino out of 1 offspring = 1/4
1 albino out of 2 offspring = 3/8 (6/16)
1 albino out of 3 offspring = 25/64
I'm not sure how you got to the 1/137,438,953,472 figure but it doesn't seem right. I know 137,438,953,472 is the square root of 18,889,465,931,478,580,854,784 which is the total number of possible outcomes there is a single gene, het x het breeding with 37 babies but I don't see how that relationship plays a part.