**ABCDE**is called a hill number if the digits

**B**and

**D**are each equal to the sum of the digits to their immediate left and right, that is,

**B**=

**A**+

**C**and

**D**=

**C**+

**E**. (Each of the capital letters in bold denotes a digit from 0 to 9, whether same or different.)

Determine the probability that x is a hill number, given that x is a base ten positive integer chosen at random between 10000 and 99999 inclusively.