Get average and percentage non zero value

How to calculate percentage non zero value occurrence base on value col 1 and 2

2017 a 0
2017 a 2
2017 a 4
2017 a 2
2017 a 0
2017 b 2
2017 b 6
2016 a 2
2016 a 2
2016 b 2
2016 b 8
2016 b 0
2016 b 0
2016 c 2
2016 c 2
2016 c 0

i manage to get average

# awk '{A[$1$2]++;B[$1$2]+=$3}END{for(X in A){print X,B[X]/A[X]}}' test
2016a 2
2016b 2.5
2017a 1.6
2016c 1.33333
2017b 4

what i want is another value base on = count record if col3 value>0 /count all record with same group ( ie, 2016a has 2 record larger then 0 so 2/2 =1)

2016a 2 1
2016b 2.5 0.5
2017a 1.6 0.6
2016c 1.33333 0.33
2017b 4 1
awk '{A[$1$2]++;B[$1$2]+=$3; if ($3>0) C[$1$2]++}END{for(X in A){print X,B[X]/A[X],C[X]/A[X]}}' infile