The path of least resistance
The current will mostly flow through the capacitor at the beginning because at time=0 the capacitor isn't full and basically looks like a short to the circuit. Since it looks like a short to the circuit, it charges very quickly. As the capacitor charges, it starts to look like an open circuit though. You could think of it as a variable resistor that starts at 0 and goes up to infinite as you charge it.

Once the capacitor is charged, the resistance is infinite and all of the current will flow through the resistor instead of the capacitor.