Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{ ightarrow}mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{ ightarrow}mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${cdots}$ < $t_n$ < $t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{leq}p{leq}{infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions which have the form $${int}_{L_2[0,t]}{{exp}{i(v,x)}d{sigma}(v)}{{int}_{mathbb{R}^r}};{exp}{i{sum_{j=1}^{r}z_j(v_j,x)}dp(z_1,{cdots},z_r)$$ for $x{in}C[0,t]$, where ${v_1,{cdots},v_r}$ is an orthonormal subset of $L_2[0,t]$ and ${sigma}$ and ${ ho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.