A box contains five cards numbered 1, 2, 3, 4, and 5. Two cards are drawn sequentially without replacement. Consider the following three events:

• $E_1$: The first card drawn is an even number.
• $E_2$: The sum of the two cards is an even number.
• $E_3$: The product of the two cards is a multiple of 3. Calculate the conditional probability $P(E_1 \cup E_2 \mid E_3)$.