a[b] = b = 0; 

1. array indexing operator has higher precedence then assignment operator (see this answer):

   (a[b]) = b = 0;

2. According to 15.26. Assignment Operators of JLS

There are 12 assignment operators; all are syntactically right-associative (they group right-to-left). Thus, a=b=c means a=(b=c), which assigns the value of c to b and then assigns the value of b to a.

(a[b]) = (b=0); 

3. According to 15.7. Evaluation Order of JLS

The Java programming language guarantees that the operands of operators appear to be evaluated in a specific evaluation order, namely, from left to right.

and

The left-hand operand of a binary operator appears to be fully evaluated before any part of the right-hand operand is evaluated.

So:

a) (a[b]) evaluated first to a[1]

b) then (b=0) evaluated to 0

c) (a[1] = 0) evaluated last

a[b] = b = 0; 

1. array indexing operator has higher precedence then assignment operator (see this answer):

   (a[b]) = b = 0;

2. According to 15.26. Assignment Operators of JLS

There are 12 assignment operators; all are syntactically right-associative (they group right-to-left). Thus, a=b=c means a=(b=c), which assigns the value of c to b and then assigns the value of b to a.

(a[b]) = (b=0); 

3. According to 15.7. Evaluation Order of JLS

The Java programming language guarantees that the operands of operators appear to be evaluated in a specific evaluation order, namely, from left to right.

and

The left-hand operand of a binary operator appears to be fully evaluated before any part of the right-hand operand is evaluated.

So:

a) (a[b]) evaluated first to a[1]

b) then (b=0) evaluated to 0

c) (a[1] = 0) evaluated last