Main.java

   public static int[] algoFunc(int[] numArray) {


       int totalMultiplication   = 1;

       for(int num : numArray) {
           try{
               totalMultiplication   = totalMultiplication   * num;
           }catch (ArithmeticException e){
               totalMultiplication   = 0;
               break;
           }

       }

       int arrayLength = numArray.length;
       int[] newArray = new int[arrayLength];
       for(int i = 0 ; i < arrayLength ; i++) {
           if(numArray[i] == 0) {
               int multiplier = 1;

               //This comment encloses the short code I could come up with to solve the algorithm but I believe

               for(int j = 0 ; j < arrayLength ; j++) {
                   if(j == i) continue;
                   try{
                       multiplier =  multiplier * numArray[j];
                   }catch (ArithmeticException e) {
                       multiplier = 0;
                       break;
                   }
               }
               //it's madly inefficient when the array does not contain 0.
               //Hence my solution.
               newArray[i] = multiplier;
               continue;
           }

           try {
               newArray[i] = totalMultiplication  /numArray[i];

           }catch (ArithmeticException e){
               newArray[i] = 0;
           }

       }

       return newArray;
    }

Thank you @meekg33k for conducting Algrorithn Fridays.
I currently can't think of any better solution, I'm looking forward to the published solution.
It'll be really informative and interesting to see the best eay to solve this without a nested loop.