In a leap year, the probability of getting $53$ Sundays is

1. A leap year contains exactly $366$ days.2. Convert the days into weeks:
$$366\text{ days}=52\text{ weeks}\times 7\text{ days/week}+2\text{ days}=364\text{ days}+2\text{ remaining days}$$
The 52 full weeks guarantee exactly 52 Sundays. To get 53 Sundays, one of the 2 remaining days must be a Sunday.The 2 remaining consecutive days can be any of the following 7 combinations:(Monday, Tuesday)(Tuesday, Wednesday)(Wednesday, Thursday)(Thursday, Friday)(Friday, Saturday)(Saturday, Sunday)(Sunday, Monday)Out of these 7 possible outcomes, Sunday appears in exactly 2 combinations: (Saturday, Sunday) and (Sunday, Monday).Therefore, the probability of getting 53 Sundays is $\frac{2}{7}$.