ID col1  col2  x
    1   Ball  a   No
    2   NA    c   Yes
    3   Bat   b   Unknown

mutate(x = case_when(
      is.na(col1) == TRUE ~ "Yes",
      !is.na(col1) == TRUE & (col2 %in% c("a", "b")|
      (col2 == "YES" & x == "Unknown" ) == TRUE ) ~ "No"),
TRUE ~ "Unknown"
))