Here is how a composted image looks like when adding Ambient Occlusion to it.

we start with a simple Shading netwrok, for this case I used Lambert shader.

Using ambient occlusion node within Maya, we ad the AO in the mental ray section of the SG node

The result render would be something ike this.

When adding the AO in the Ambient swatch in the shader node, rather than the SG Shader node, you end up with color overexposure.

If you lower the Diffusion to 0

The correct way of doing it in composting package would be using a “multiplier node”
So to achieve that in Maya, we will use the following shading network

mib_illum_lambert > multiplyDivide Input 1
mib_amb_occlusion > multiplyDivide Input 2
multiplyDivide > Materal Shader in the SG node

you might notice a slight difference but that because I used a mib_illum_lambert instead of Lambert, and it render differently.