Why does the carbs / fiber ratio decrease after cooking?
When you cook things using water you add mass that have 0 calories. Some food, like rice, absorb that water. Hence boiling 100 grams of rice increase final mass to around 300 grams.
Then again you measure the 100 grams carbs and it's 3 times less than your starting points because you never added additional carbs in the process. 

The fiber amount is IMHO wrongly calculated because 3,4 gram divided by 3,16 (ratio of carbs in 100 grams before and after cooking) is 1,075. Probably someone rounded up the 75 wrong and had 1,8 instead of 1,08.